The fifth term in the expansion of the binomial (a +b)" is given by 10 p° (29)". Write down the value of n. 4. a. 10 c. 14 b. 15 d. 4

Q: The coefficients of three consecutive terms in the expansion of (1 + ay" are in the ratiol: 7:42.…

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Q: Find the first three terms of the expansion (4 – 2x)°. a. 45(1+ 쪽+ +…) O b. 4(1- + O c. 2°(1+ % + +…

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Q: Q2/ Fin x in the

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Q: EX1 FIND THE 4th TERM BINOMIAL EXPANSION (3x+2y) ³ IN THE OF 3

A: The given expression,      3x+2y5

Q: Find the coefficient of th 'u in (r + y 5

A: *to find:- coefficient of x^2*y^3.

Q: 7. Apply Lagrange interpolation formula to find k, given that P2(3) = 35 2 5 f (x) 2 k 275

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Q: Find the coefficient a of the term in the expansion of the binomial. Binomial Term (z? – t)12 a =

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Q: Use the binomial formula to find the coefficient of the y^3 m^17 term in the expansion of (3y- m)^20

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Q: b) In this part you will show that for each positive integer n, F? – Fr+1 F-1 = (-1)*+!. Show that…

A: We prove, by induction, that (Fn – 1)(Fn + 1) – (Fn)^2 = (-1)^n for all positive integers n, where…

Q: 3. The third term in the expansion of (x +p ) is 252r°. Find the possible values of p. а. +4 с. +2…

A: Given that the third term of the expansion of  (x+p)8 is 252x6. We find all possible values of p.

Q: a. Use your values of a, b and c to find the term independent of x in the expansion of 5 1 (2 + 9x)2…

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Q: 12. What is the coefficient of x³y® in the expansion of (-3x + 5y)*? a) C(13,5) · 38 . 55 b)…

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Q: Calculate the following by Binomial Theorem up to two decimal places. Q.7 (1.02)'º Q.8 (1.04)

A: NOTE: According to the guidelines, we can only answer the first question out of multiple questions…

Q: 10 Find the term involving y³ in the expansion of 2x – Select one: O a. 924x2y3 O b. 636x2y³ O c.…

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Q: What is the coefficient of xy- (the third term) in the expansion of (2x + 3y)'? 6. O -18 O 18 O 54

A: We have to find the coefficient of xy2 in the expansion of 2x+3y3.

Q: 1 nd the term involving x13 in the expansion of 4x? + c. 524812286 d 624812288 524812288 544812288

A: We are asked to  find the coefficient of x13

Q: Find the middle term in the binomial expansion of (x–1). Select one: a. 20x O b. 15x* none of these…

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Q: When the expression given below is opened according to the binomial theorem, what is the value of…

A: Introduction: The binomial expansion of the term (a + b)n for n ≥ 0 is given as follows:

Q: M d formulas for the entries of M", where n is a positive integer.

A: To find the power of a matrix

Q: Express (1:1)⁴ as a binomial of the form (a+b)^n and evaluate it

A: To find the binomial expansion and evaluate it

Q: 1. Which of the following expression(s) are third-degree binomials? Select all that apply. А 2у —…

A: From the given equations we will write degree of each expressionDegree means the highest power in…

Q: B. Solve for the indicated term of each expansion. 3. The term involving x* of (+52

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Q: 7. In the expansion of px (5+px), the coefficient of the term in x° is 3402. Find the value of p. а.…

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Q: Find the first three terms of the expansion (4 – 2x)°. O a. 2°(1 – + + .) O b. 45(1+ 쪽 + 쪽 + ) 5x2 O…

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Q: Use the first 3 terms in the expansion of (2+5x)6 to approximate the value of (2.05)6

A: We know that a+bn = C0nan-0b0 + C1nan-1b1 + … + Cnnan-nbn

Q: a)What is N? lo) What is Sx?

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Q: xa3 + ya? (a + 1)* – (a – 1)* (a + 1)4 + (a – 1)4 9- za* + ta? + 1

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Q: The first three terms in the expansion of (1 + ay)^n are 1, 12y, and 68y^2. Find a and n.

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Q: 4. You are given: 7800-70t- 1? P30 0SIS TO 7800 Find qso-Hs0-

A: The given formula for tp30 represents the probability of an individual aged 30 years to survive the…

Q: (a) Use Newton's binomial theorem to calculate √50 with 4 terms. (b) What is the coefficient of rir,…

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Q: The 3rd term in the expansion of (y?+2/y)21 and the 3rd term in the expansion of (y+%)7 are equal.…

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Q: Find AC B T. 4

A: Apply the property of the triangle then find the value of the AC

Q: W 4. What is the value of the 4th term of the expansion (a + b)"? O a5 O 5a*b O 10a²63 10a b?

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Q: Expand the following using the Binomial Theorem or Pascal's Triangle: (4r – 2y)' 64x – 96x²y + 48xy²…

A: 4x-2y3 Binomial theorem is, For any positive integer n,…

Q: Find the fifth term in the expansion (3x+4y)8 A. 840x4y4. В. 840х у3. ,5, C. 3360x³y5. С. D.…

A: Expansion using bionomial theorem

Q: Find the largest value of n such that: Σ E (9k – 5) < 3000 k=1 n =

A: We expand the sum and use the know formulas of "sum of first n integers"

Q: For Exercise, find the indicated term of the binomial expansion. (2c2− 5)9; Term containing d25

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Q: -1)º-k(x)' 18-6k 2512 k=0

A: to calculate the terms first we need to understand the calculation of 0! = 1 1! = 1

Q: 2. A toy company sells 3-packs of sphere-shaped bouncy balls. If the company ships the three bouncy…

A: Finding the empty space in the given figure.

Q: 12. When written in descending powers of z, the third term in the expansion of (2x +w)* is 156.8a.…

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Q: 15. The following shows a pattern made with matchsticks. Based on the pattern, what would be the…

A: In 1st pattern , no. Of matchstick= 3 In 2nd pattern , no. Of matchstick = 8  In 3rd pattern, no. Of…

Q: 5. (a) Find a formula for the number of square tiles in the figures below. n= 1 n= 2 n= 3 n= 4

A: To find a formula to determine the number of square tiles in the given figures.

Q: The binomial approximation can also be written: (1 + eps)^n = 1 +n (eps). Use this to approximate…

A: Solution: Consider the given number x = 1.04 Also, it is given that binomial approximation can also…

Q: Which of the following is the correct expansion of (y + 1)(12y2 + 2y + 6)?

A: The given term is y+112y2+2y+6

Q: Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm…

A: Explained below

Q: Find the first three terms of the expansion (4 – 2x)°. 4°(1 + 쫄 + 폴 + .) * + +..) Oc 4°(1-쪽 + 폭+ …)…

A: The solution is given as

Q: 2) Find the Middle term(s) in each the following expansions : E+x) • * (3x – 2y2)7 8

A: (a) x+1x28 number of terms is even, so middle term will be 82+1=5th term. Now, Tr+1=nCran-r(b)r here…

Q: Which of the following statements are true (as n gets large or n → 0)?

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Q: Find the Middle term(s) in each the following expansions : * (z+)" • (3x-2y2)7 8.

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Q: 3. The binomial coefficients can be calculated directly by using the formula So

A: The binomial coefficients can be calculated directly by using the formulank=n!k!(n-k)!