Graduate. This sequence is known as Pascal's triangle. 2. (12) 6. May 1, 2024 · Then, Binomial distribution is a Taylor expansion of a binomial (q + p)n where n (# of trials) is the order of interest, and r (# of successes) is the parameter defining the dominating term through. C2 SEQUENCES AND SERIES Answers - Worksheet C 1 4a = 1 + 4x + 6x 2 + 4x3 + x b = 1 − 5x + 10x − 10x3 + 5x4 − x5 c = 1 + 3(4x) + 3(4x)2 + (4x)3 d = 1 + 3(−2y) + 3(−2y)2 + (−2y)3 = 1 + 12x + 48x2 + 64x3 = 1 − 6y + 12y2 − 8y3 e = 1 + 4(1 2 x) + 6(1 2 x)2 + 4(1 2 x)3 + (1 2 x)4 f = 1 + 3(1 3 y) + 3(1 3 y)2 + (1 3 y)3 = 1 + 2x + 3 2 To get an approximation you can consider a few terms from the expansion. and the last term is bn. 10 Arithmetic Series: Finding a and d. --> (2+5x)⁹ = 2. \displaystyle {\left ( {a}+ {b}\right)}^ {5} (a +b)5. (3) (d) Find the sum to infinity of the sequence. Answer. Experienced Mathematics Tutor for GCSE, A levels and IB. 9. Find the first 3 terms, in ascending powers of x, of the binomial expansion of binomial theo - Free download as PDF File (. All C1 Revsion Notes. 3: Geometric Sequences and Series A geometric sequence, or geometric progression, is a sequence of numbers where each successive number is the product of the previous number and some constant r . 4 Infinite Figure 2. Binomial Expansion Series, Sequences, and Binomial Expansion Test Calendar Subject to Change! HW 1: HW 7: Answer all questions in #1 – 6: 1. Solomon Press. This topic is included in Paper 1 for AS-level Edexcel Maths and Papers 1 & 2 for A-level Edexcel Maths. (i) Given that . (2) (Total 9 marks) (b) The first four terms of the binomial expans ion of in ascending powers of x are 1 + ax + bx 2 + cx 3. a Find the first 4 terms, in ascending powers of x, of the binomial expansion… In the binomial expansion of (1 + x)40, the coefficients of x4 and x5 are p and q respectively. x, of the binomial expansion 5. g. In the [latex]n\text {th} [/latex] row, flank the ends of the row with 1’s. Show Solution. 1 Binomial Expansion for the AQA A Level Maths: Pure syllabus C2 SEQUENCES AND SERIES Answers - Worksheet D page 4 Solomon Press 13 a12 + 12(3 = 311)(− 3 x) + 12 11 2 × (310)(− 3 x)2 + 12 11 10 32 ×× × (39)(− 3 x)3 + … = 531 441 − 708 588x + 433 026x2 − 160 380x3 + … b let 3 x = 0. The sum of the exponents on any term is n. Binomial Expansion 1a. 2 + x k , where k is a constant. £55 / hour. (b) Use your expansion to estimate the value of (1. Thus, if we denote the terms of a binomial by a and b, the square of a binomial gives after expanding it. Solution: Let us take a = 3 and b = 2x in the binomial expansion of (a + b) 10. a) Binomial Expansion 1 b) Binomial Expansion 2, c) Geometric Sequences 1 ,d) Geometric Sequences 2. x. It should also be obvious to you that (a + b)¹ = a + b . 3√8−2x 8 − 2 x 3 Solution. May 17, 2017 · Divergence simply means "not convergence". 0 license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. 001 2) Substitute in the x value into the Expansion. Dec 11, 2010 · C2 Sequences Series: Binomial Expansion PhysicsAndMathsTutor. Define geometric sequence as a sequence in which each term after the first is found by multiplying the preceding term by a constant ratio. in this expansion is 525, (b) find the possible values of C2 - Sequences and Series OCR, AQA, Edexcel 1. Next use the formula to determine the 50th partial sum of the given arithmetic sequence. Nov 17, 2022 · This page titled 7: Sequences and Series, Mathematical Induction, and the Binomial Theorem is shared under a CC BY-NC-SA 3. We call these numbers the terms of the sequence. b Use your series expansion with a suitable value of x to obtain an estimate for 2. (4) Given that the coefficient of x2 is 6 times the coefficient of x, (b) find the value of k. Infinite Geometric Series , where we add all of the terms in the geometric progression. Taking bookings for study leave, summer and 2024-2025. Solution: ( 2 +x a ) 3 has coefficients 1 3 1 The circled number is the coefficient of the term 21 (x a ) 2. This expansion is only valid when. 2: Arithmetic Sequences and Series; 9. (2) (c) Find the sum of the first 15 terms of the sequence. + 9x + px2 + qx3, 12x < 1. Prove that S = Xn k=1 a k = 1 2 n(2a+ (n 1)d): [8] Hint: this is a proof that you may have seen in class. Example 1 Use the Binomial Theorem to expand (2x−3)4 ( 2 x − 3) 4. Show Step-by-step Solutions Binomial Expansion 1a. Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost. Hint: use Pascal’s triangle and binomial expansion: (a) x4 + 4x3 + 6x2 + 4x+ 1. The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. The binomial expansion Exercise A, Question 6 © Pearson Education Ltd 2008 Question: The coefficient of x2 in the expansion of ( 2 + ax ) 3 is 54. ) If we wish to expand an expression of the form , then we can use the above formula by replacing every with . In an arithmetic progression the sum of the first ten terms is 400 and the sum of the next ten terms is 1000. In the previous chapter (but not only), we also have explained how to expand the square and the cube of a binomial. 0000065104166. (2) (Total 6 marks) 2. And so we get the answer: X1 k=1 4 1 6 k = 24 5 4 = 4 5 [4] 10. Model Answers. 1 Binomial Expansion for the OCR A Level Maths: Pure syllabus D1-1 9 Binomial Expansion: EXTENSION Extending Binomial Expansion D1- 20 Binomial Expansion: Writing (a + bx)^n in the form p(1 + qx)^n D1- 21 Binomial Expansion: Find the first four terms of (1 + x)^(-1) All A level questions arranged by topic. in ascending powers of . 3 2 (2) (b) Find the first term of the sequence. 4 3 + x(1 12 ) in ascending powers of up to and including the x term in x3 is 1 + 9x + px2 + qx3, 12x < 1. 3 Geometric Sequences and Series 418 8. Revision notes on 4. 025)8, giving your answer to 4 The third term of a geometric sequence is 324 and the sixth term is 96 (a) Show that the common ratio of the sequence is . 03 (2dp) Solomon Edexcel Worksheets and answers for the C2 module. 1b 2 C2 2017 1 4. 1 anything that cancels to 2 Simplified —Xx2 — x Attempt to substitute 0. Figure 12. The binomial expansion of (1 + 12 x ) 3. 43 JEE Main Mathematics Online (2019-2012) & Offline (2018-2002) Chapter-wise + Topic-wise Solved Papers 3rd Edition 2011-03-08 Brooks/Cole. [5] 11. 4. SEND. For problems 3 and 4 write down the first four terms in the binomial series for the given function. P(r / n) = ∑ni = 0Cniqn − ipiδir = Cnrqn − rpr. Therefore, the general term is an = 5n − 1. 13 a Expand (3 – 3 x)12 as a binomial series in ascending powers of x up to and including the term in x3, giving each coefficient as an integer. (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3. Find the series expansion of f(x) in ascending powers of xup to and including the term in x3and state the set of value of x for which it is valid. txt) or read online for free. p5q4 term of (3p + q)9. (4) (Total 9 marks) (a) (i) Using the binomial expansion, or o therwise, express (2 + y)3 in the form Geometric Sequences and Series. Show Step-by-step Solutions In the previous chapter (but not only), we also have explained how to expand the square and the cube of a binomial. 4. 528 Chapter 8 Sequences , Series , and Probability. (a) Find the first 4 terms, in ascending powers of . The exponents on a decrease by one on each term going left to right. Now, the Binomial Theorem required that n n be a positive integer. a4b2 term of (2a + b)6. a n. a . 0. [4] Showing top 8 worksheets in the category - Binominal Expansion. y3 term of (y + 5)4. 14 a Expand (1 – x)5 as a binomial series in ascending powers of x. b n. 1 −. 1b 3 C2 2015 1 4. the Binomial Theorem 8. com Edexcel Internal Review 1 1. co. c= 1 + 3(4x) + 3(4x)2+ (4x)3d= 1 + 3(−2y) + 3(−2y)2+ (−2y)3. 2 Arithmetic Sequences and Series 409 8. (4) (b) Use this expansion with your values of p and q together with an appropriate value of x C2 Sequences & Series: Binomial Expansion www. To generate Pascal’s Triangle, we start by writing a 1. 99812 ≈ 531 441 − 4251. 3 (i) Find and simplify the first four terms in the binomial expansion of (1 + x) 10. (a + b) 2 = a 2 + 2ab + b 2. f(x) =3+5𝑥𝑥 (1+3𝑥𝑥)(1+𝑥𝑥)2. 4: Binomial Theorem The binomial theorem provides a method of expanding binomials raised to powers without University of Glasgow - MSc Astronomy and Physics. 1 3 marks. 97468099. where b is a non-zero constant. June 2010 qu. The binomial expansion of . The binomial coefficients are the integers calculated using the formula: (n k) = n! k!(n − k)!. (4) (c) Hence find the coefficient of x in the expansion of . Find the possible values of the constant a. = 1 + 12x+ 48x2+ 64x3= 1 − 6y+ 12y2− 8y3. C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. e= 1 + 4(1 2. Book Tutor. Use Pascal’s triangle to quickly determine the binomial coefficients. Dec 27, 2014 · C2 Sequences & Series: Binomial Expansion 1. 792 Binomial Expansion of (ax±b) n, Where n is a Positive Integer. Find the common difference and the first term. You can find Edexcel International A-level P2 (WMA12), C12 (WMA01), and Edexcel A-level old spec C2 (6664), past papers, mark schemes and model answers below: expand. < 1 35 terms of the series. x, of the binomial expansion Free Binomial Expansion Calculator - Expand binomials using the binomial expansion method step-by-step Apr 6, 2018 · C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. Sequences and Series Key Skills Section (for selecting more than one) Jan 24, 2012 · The Sequence and Series chapter in c2, is quite big, so I will divide it into 3 / 4 posts. This topic is included in all papers for AS-level and A-level OCR (MEI) Maths. 001) + 115200(0. When we take the sum of the terms in a sequence, we get a series. 1. 002 ∴ x = 0. Find the first 3 terms, in ascending powers of x, of the binomial expansion of. Let’s take a quick look at an example. 3a. Consider an arithmetic sequence with kth term given by a k = a+ (k 1)d. The larger the power is, the harder it is to expand expressions like this directly. (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of (1 + ax)7, where a is a constant. Some of the worksheets displayed are Binomial expansion work, The binomial expansion, Binomial expansion question work, Sequences and series part 1b binomial expansion, The binomial theorem, Binomial expansions exam questions, Work the binomial theorem, C2 the binomial theorem work Maths/Physics Examiner Who Has Helped 6 GCSE/IB & 8 A Level Students Acheive A*'s In Last Year Alone. (2) Given that the third term of this series is 540x 2 , (b) show that k = 6, (2) (c) find the coefficient of x 3. 1 Key Facts: Informal Binomial Expansion A binomial is a polynomial that is the sum of two terms (e. For instance, 2,4,6,8 are the first four terms in the sequence of even positive integers. pdf), Text File (. Find the value of p and the value of q. E: Sequences, Series, and the Binomial Theorem (Exercises) is shared under a CC BY-NC-SA 3. The first two numbers in the Fibonacci sequence are 1, and each successive term is the sum of the previous two. . To calculate the 50th partial sum of this sequence we need the 1st and the 50th terms: a1 = 4 a50 = 5 − 1 = 249. 23 Use the Binomial Theorem to Expand a Binomial. Answer: 2, −4, 8, −16, 32. 𝑎𝑎𝑎𝑎+ 𝑏𝑏). In the 3 rd row, flank the ends of the rows with 1’s, and add [latex]1+1 [/latex] to find the middle number, 2. Nov 16, 2022 · This is useful for expanding (a+b)n ( a + b) n for large n n when straight forward multiplication wouldn’t be easy to do. The first term is an. The New 2017 A level page. 588 936 − 0. A sequence (or series) is divergent if and only if it is not convergent. 005⁹ --> ∴ x = 0. Nov 16, 2022 · For problems 1 & 2 use the Binomial Theorem to expand the given function. (i) (ii) (iii) How did you do? View Answer. Sep 19, 2022 · Help Center Detailed answers to any questions you might have Using the binomial expansion for $ sequences-and-series; Feb 14, 2022 · The real beauty of the Binomial Theorem is that it gives a formula for any particular term of the expansion without having to compute the whole sum. [2] 10. Three consecutive terms of an arithmetic series are a, b, and (3a + 4) respectively. (4) (b) Use this expansion with your values of p and q together with an appropriate value of x to obtain an estimate of (1. 528 + 15. x6 term of (x + 2)8. (a) Find the value of p and the value of q. where k is a constant. (2) (Total 6 marks) 4. (4+3x)5 ( 4 + 3 x) 5 Solution. b the value of the coefficient of x3 in the expansion. In the following exercises, find the coefficient of the indicated term in the expansion of the binomial. For example. 03 (2dp) an = a1 + (n − 1) d = 4 + (n − 1) ⋅ 5 = 4 + 5n − 5 = 5n − 1. [3] (ii) Given also that the coefficient of . 1 Into a candidate's binomial expansion. [2] (b) x3 17. (2) (Total 6 marks) For the binomial expansion, in descending powers of x, of; 12 3 2. 15. 1b 4 C2 June 2014R 1 4. and . are both positive, show that . Questions are taken from the pre 2010 exam papers. Find an expression for b in terms of a. London Science College © 2024 Geometric Progressions, where we multiply by a fixed number to get each new term of the progression. 0003125 1. where P(r / n) is the probability to observe the event r / n of r successes out of n trials. x) + 6(1 2. 1b 17. Oct 6, 2021 · This page titled 9. x)2+ 4(1 2. This question is missing context or other details : Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. Find the first 4 terms of the binomial expansion, in ascending powers of x, of :1+𝑥 4 ;8 giving each term in its simplest form. (2) b. Pascal’s Triangle. Jan 2, 2012 · C2 Edexcel Core Mathematics January 2012 Question 3 Binomial Expansion 3. 1 Binomial expansion 1. Notice, that in each case the exponent on the \(b\) is one less than the number of the term. As a farmer bales a Transcript. C2-Sequences-Series-C-Simple-Binomial-Expansion-Answers. Key Skills. 1 9746810 2 0. a. All C3 Revsion Notes. 99812, giving your answer to 2 decimal places. 025) 8 giving your answer to 4 decimal places. Find the values of the constants a, b and c. The binomial theorem provides a method for expanding binomials raised to powers without directly multiplying each factor: (x + y)n = n ∑ k = 0(n k)xn − kyk. 5E. in the expansion is 128, find the values of . Follows correct answer with 27 90x+120x2 can iswhere (sp marks for correct answer Misreads ascending and gives —32x5 + 240x4 — 720x3 is marked as BIBOMIAO special case and must be completely correct (If any slips could get BOBOMIAO) Ignores 3 and expands (1 ± 2x)5 is 0/4 243, -810x, 1080x2 is full marks but243, -810, 1080 is GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. k . Consider a geometric sequence with kth term a k = ark such that: a 1 = 1; X1 k=0 ark = 9 2: (a)Either a = 3 and r = 1 3, or a = 3 2 and r = 2 3. 006 2. 97 10. The Binomial Expansion, is a theorem which allows us to expand (a + b)^n, where n is an integer. 1st class MSci Astrophysics. Sequences and series - Binomial series PhysicsAndMathsTutor. Find the first 4 terms, in ascending powers of x, of the binomial expansion of. And the sum $1-1+1-1+\cdots$ is not convergent, because the sequence of its partial sums (which is $1,0,1,0,1,0\cdots$) is not convergent (because it does not have a limit). x , } expansion With candidate' s followed through ( ** x) Award SC Ml if you see Either 2 {1. 4 in ascending powers of x up to and including the term in x3 is. Therefore, the general term is expressed in terms of the previous two as follows: F n = F n − 2 + F n − 1. Expand the following expressions. 2 = (1 − 2 )1 2. Use your expansion to estimate the value of (1. (a) Find the first 4 terms, in ascending powers of x, of the binomial… AS and A level Mathematics Practice Paper – Binomial expansion – Mark scheme 5 Source paper Question number New spec references Question description New AOs 1 C2 2012 1 4. aectutors. Experienced, full-time, online tutor. (4) (b) Use this expansion with your values of p and q together with an appropriate value of x = 4. But with the Binomial theorem, the process is relatively fast! Created by Sal Khan. Symbolise this as a, ar, ar²,…. b) Use the first three terms in the binomial expansion of ( )2 3− x 10, with a suitable value for x, to find an approximation for 1. 034 642 080 = 527 205. For example, 2+4+6+8+ is a series. in the expansion. Then, x6 will appear in the term containing (2x) 6 and nowhere else. The first three terms in the expansion of (1 + ax)b, in ascending powers of x, for |𝑎𝑎| < 1𝑥𝑥, are 1 – 6x+ 24x2. Jan 3, 2023 · A sequence is simply a list of numbers in a particular order. All C4 Revsion Notes. Term in x2 is 3 × 21 × (x a ) 2 = 6a2x2 C2 SEQUENCES AND SERIES Answers - Worksheet D page 4 Solomon Press 13 a = 312 + 12(311)(− 3 x) + 12 11 2 × (310)(− 3 x)2 + 12 11 10 32 ×× × (39)(− 3 x)3 + … = 531 441 − 708 588x + 433 026x2 − 160 380x3 + … b let 3 x = 0. 1 Infinite Sequences 401 8. (5) 4. 7 Feb 19, 2024 · The number of terms is n + 1. (a) Find the first 4 terms of the binomial expansion, in ascending powers of x, of (1 + x/4)8 giving each term in its simplest form. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team. (a) Find the first 4 terms, in ascending powers of x, of the binomial… In the binomial expansion of (k + ax)4 the coefficient of x2 is 24. 10C6 a4b6 = 10C4 a4b6 10 × 9 × 8 × 7 4 =. Notice that this corresponds to picking the first two terms from the binomial theorem expansion (1 + x)n = 1 +(n1) x +(n2) x2 + ⋯ +xn. 6352 (NP: If it only mentions to use y terms in the question, you only need to add together y terms in the answer) C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. Pearson Education accepts no responsibility whatsoever for the accuracy or method of working in the answers given. k. University of Bristol - MEng Mechanical and Electrical Engineering. (a) Find the first 4 terms, in ascending powers of x, of the binomial… C2-Sequences-Series-C-Simple-Binomial-Expansion-Answers. 001)² --> 523. 0 license and was authored, remixed, and/or curated by Carl Stitz & Jeff Zeager via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. P2 | C12 | C2. Find the first 3 terms, in ascending powers of x, of the binomial expansion Jun 20, 2020 · C2 Sequences Series: Binomial Expansion Edexcel Internal Review 1 1 a Find the first 4 terms in ascending powers of x of the binomial expansion of 1 + ax7 where a is a constant… May 27, 2024 · Get Sequences and Series Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. --> 512 + 11520x + 115200x² --> 512 + 11520(0. Feb 14, 2022 · Exercise 12. [4] C2 Sequences and Series. The Binomial Theorem, where we learn how to expand expressions like. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 + kx)7. C2 SEQUENCES AND SERIESAnswers - Worksheet C. com. x7 term of (x − 3)9. Here is a set of practice problems to SEQUENCES AND SERIES Answers - Worksheet C. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Jan 2009 qu. 14a= 1 + 4x+ 6x2+ 4x3+ xb= 1 − 5x+ 10x− 10x3+ 5x4−x5. r. Familiarise with the formulae of a geometric sequence: nth term = ar^ (n - 1) and sum of first n terms = a (1 - r^n) / (1 - r) when. 5 Find the coefficient of x6 in the expansion of (3 + 2x) 10. 1 Binomial Expansion for the Edexcel A Level Maths: Pure a) Determine, in ascending powers of x, the first three terms in the binomial expansion of ( )2 3− x 10. $\endgroup$ – Oct 11, 2016 · It is not currently accepting answers. 025-0. 1 Binomial Expansion for the OCR A Level Maths: Pure syllabus, written by the Maths experts at Save My Exams. 17. Questions and answers with explanations on binomial theorems Sequences and series - Binomial series PhysicsAndMathsTutor. Formula Book. For instance, for "small" x, 1 + nx is a "reasonable" approximation for (1 + x)n. Give each term in its simplest form. x)12 as a binomial series in ascending powers of x up to and including the term in x3, giving each coefficient as an integer. C2 Sequences and Series. c) Use the answer of part (b) to estimate, correct to 2 significant figures, the C2 Sequences & Series: Binomial Expansion PhysicsAndMathsTutor. and for the cube of a binomial, we obtain after expanding. x . AQA Core 2 5. 3. Rewriting so the power is visible. x5 term of (x − 4)6. b. uk Edexcel Internal Review 1 1. The exponents on b increase by one on each term going left to right. You should know that (a + b)² = a² + 2ab + b² and you should be able to work out that (a + b)³ = a³ + 3a²b + 3b²a + b³ . All C2 Revsion Notes. (click to see video) One interesting example is the Fibonacci sequence. giving each term in its simplest form. (1+3x)−6 ( 1 + 3 x) − 6 Solution. Example 5. Evaluate. Find the value of (2) 4a. 1) Set the expansion expression equal to the new value. (9−x)4 ( 9 − x) 4 Solution. In the row below, row 2, we write two 1’s. ( a + b) 5. (4) Given that the coefficient of x2 in this expansion is 525, (b) find the possible values of a. This section looks at Binomial Theorem and Pascals Triangle. 1. ξ1 − 2 2, Example 1: Find the expansion of up to and including the term in and state of values for for which the expansion is valid. (4) Given that the coefficient of . ak = 2. 5. n + 1. 𝑦𝑦 We can either use the binomial formula or Pascal’s triangle to expand expressions of the form (𝑎𝑎+ 𝑏𝑏)𝑛𝑛. 1 Binomial Expansion for the AQA A Level Maths: Pure syllabus, written by the Maths experts at Save My Exams. Questions and model answers on 4. [4] (iii) Hence find the coefficient of . Download these Free Sequences and Series MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. So the term containing x6 is. We denote the terms in a sequence by Video answers for all textbook questions of chapter 14, Binomial Expansions, Sequences, and Series, Beginning and Intermediate Algebra by Numerade Get 5 free video unlocks on our app with code GOMOBILE C2 SEQUENCES AND SERIES Answers - Worksheet C 1 4a = 1 + 4x + 6x 2 + 4x3 + x b = 1 − 5x + 10x − 10x3 + 5x4 − x5 c = 1 + 3(4x) + 3(4x)2 + (4x)3 d = 1 + 3(−2y) + 3(−2y)2 + (−2y)3 = 1 + 12x + 48x2 + 64x3 = 1 − 6y + 12y2 − 8y3 e = 1 + 4(1 2 x) + 6(1 2 x)2 + 4(1 2 x)3 + (1 2 x)4 f = 1 + 3(1 3 y) + 3(1 3 y)2 + (1 3 y)3 = 1 + 2x + 3 2 C2 SEQUENCES AND SERIES Answers - Worksheet A 1 a r = 3 b r = 1 4 c r = −2 u8 = 3 × 3 7 = 6561 u 8 = 1024 (a) Find the first four terms, in ascending powers of x, in the binomial expansion of 5. The Binomial Series. Let’s look for a pattern in the Binomial Theorem. com Edexcel Internal Review 1 . zb ul zy va rj bv qv yr el lp