3. a) Obtain the expansion for (3 + 2x)* in ascending powers of x b) Find the term independent of x: 3 G- 5x³ ) 10 2 c) Obtain the expansion of: 1-3x2 up to the term in x8

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: Expand (7 – 3x)“ in ascending powers of x, up to and including the 4" term. Hence, approximate…

A: We know (n+1)! = (n+1) n! Crn = n!(n-r)! r!

Q: 16. The expansion of (2 + 3x;-1 is valid when >x>

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Q: 2x+ 3 2 X 6

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Q: (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x?.

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Q: S@ Find the coefficient f e in the expansion of (1-4x)2 for all non-negative integers n 6 Using…

A: Given that, (a) The expansion of 1-4x-12. Calculate the coefficients of xn. (b) Prove that…

Q: The coefficient of x-y* in the expansion of (4x-y)° is 240. O True

A: Given: the coefficient of x2y4 in the expansion is 240

Q: What is the 5th term in the expansion of (x^3-1/x^2)^10?

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Q: Use binomial theorem to expand (2+X)5 in ascending powers of x up to the terms containing x3  and…

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Q: Give a combinatorial interpretation of the coefficientof x6 in the expansion (1 + x + x2 + x3 +⋯)3.…

A: According to the given information, it is required to give a combinatorial interpretation of the…

Q: 4. Find the 11th term in the expansion of 25 3r- + 5.x

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Q: Find the coefficient of x4 in the expansion of 1 +

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Q: Find the term indicated in the expansion .

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Q: Let k, n be positive integers with k < n. Give a combinatorial proof of the identity (in the form…

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Q: Find the coefficient of x5in the expansion of (1 – 2x + 3x2)5

A: I have solved Algebraically

Q: Find the Term that free from x of the expansion (x2 +10

A: Given expansion(x2+(2/x3))10 a=x2 and b=2/x3, n=10 Formula  General term formula is, Tr+1= nCr…

Q: Give a combinatorial interpretation of the coefficientof x4 in the expansion (1 + x + x2 + x3 +⋯)3.…

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Q: 6. When the terms are arranged in descending powers of x, determine the middle 10 term in the…

A: Given below the detailed solution

Q: 14 Which term of the expansion of (x + 1)contains x 16 Term number contains x16

A: The given expression is:…

Q: Which term of the expansion of (x° + 7) contains x 28 ,36 Term number contains æ36

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Q: How many terms are there in the expansion of (4.x + 7y)0.+ (4x- 7y)10 ?

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Q: 19. Determine the binomial power that when expanded is x12 x⁹ + x6 x15 + x3 1 + Show your work. 2 16…

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Q: In the expansion of 5x in descending powers of x, find the constant term in the expansion and state…

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Q: (c) Find the term independent of x in the expansion of, 15 + 4x?

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Q: 10 [1] Find the coefficient of the term involving x* in the expansion of (3x - a. -262444 b. -262440…

A: We have to find the coefficient of x^4.

Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: What is the coefficient of x^8 in the expansion of (2+x)^11?

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Q: Find the coefficient of x7 in the expansion of (x + 2)9

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Q: When the terms are arranged in descending powers of z, determine the middle 8 3 term in the…

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Q: Compute the coefficent of x8    in the expansion of (3x -2)13

A: The given expression is,

Q: 11. Find the fifteenth term in the expansion of (x2 - -) 18

A: Given that, x2-1x18 We have to find the fifteenth term in the expansion of x2-1x18, By using, The…

Q: Define a recursive sequence of complex numebers as,  g0 = 1, g2 = v,..., gn = u gn-2 +v gn-1, where…

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Q: Obtain the expansion for (3 + 2x)* in ascending powers of x

A: According to binomial expansion,  a+bxn=an+n1an-1bx+n2an-2b2x2+n3an-3b3x3+....+nn-1abn-1xn-1+bnxn…

Q: Find the first 4 terms in the expansion of (2 + x²)° in ascending powers of x.

A: Given expression: 2+x26  ……1   To find: First 4 terms (in increasing power of x) in the expansion of…

Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (3x + 1)12 The…

A: The equation is 3x+112

Q: 3) Find the Term that includes x? of the expansion (x +

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Q: Find the Term that includes x? of the expansion (x³ +°

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Q: Find the term independent of x in the expansion of 3 1 - 2r

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Q: Use the binomial theorem to identify the coefficient of x° in the expansion: (2x + 1)4

A: Consider  (2x+1)4

Q: What is the coefficient of x° in the expansion of (x + 1)14 + x² (x – 1)13?

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Q: Obtain the expansion of : 2 up to the term in x8 1-3x2

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Q: 6. Describe the left cosets of SL2(R) in GL2(R). What is the index of SL2(R) in GL2(R)?

A: For a group G with a subgroup H, the left coset is defined by gH=gh:h∈H∀g∈G.  Since g can be…

Q: Obtain the expansion of ; up to the term in x* 1-3x2

A: We know 11-x = 1+x+x2+x3+ ⋯

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

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Q: n what the coefficient of in the 13 expansion (x- 3y) of

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