In the expansion of (3x + 2y) °, the term 90, 72028 yl2 is the 4th term 5th term O 7th term O 6th term

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: The first term in the Binomial expansion of (3x-y) is: None |(3x)y |(3x)6 |(3x)®y 1

A: general term of binomial exxpanson (a+b)n is Tr+1=nran-rbr

Q: Given (x − y)108. Use the Binomial Theorem to find the coefficient of x106y2, the third term of the…

A: We have to find

Q: Determine the term involving y5 in the expansion of (3y +).

A: Please refer the attached image for complete solution. THANK YOU.

Q: Compute 7 -de using the techniques as presented in class and in our textbook. Show all the (4-x²)*…

A:

Q: What is the exponent on the x variable of the 3st/nd/rd/th term in the expansion of 17 (x2 +3y)" ?…

A: using formula:-

Q: If 6th term of a G.P. is 9375 and its 4th term is 375.Find its 9th term.

A:

Q: Find the term indicated in the expansion .

A:

Q: Find the term indicated in the expansion (x + 2y)6; third term.

A: Find the term indicated in the expansion (x + 2y)6; third term.

Q: Find the 4th term from the end in the expansion (2a + 5b)8.

A: Let's find 4th term from the end.

Q: Use Binomial Coefficients of x10y3 in the expansion of (x+2y)13.

A: Here the given expansion of (x+2y)13.  the general term of these series is

Q: 9. Given the Mac expansion of y = In(1+ x) below, use it to approximate In(0.4) to the 4th decimal…

A: To approximate ln(0.4) to the 4th decimal place accuracy using the Maclaurin expansion of y=ln1+x.

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

A:

Q: Give a formula for the coefficient of xk in the expansion of (10x + 20/x)100, where k is zero i.e.…

A: Given that 10x+20x100 The objective is to find the formula for the coefficient of xk. By binomial…

Q: Find the coefficient of the term containing x' in the expansion of (2x-y)°.

A: Binomial theorem

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

A:

Q: Use the binomial theorem to expand and simplify.

A: Given :  Expand x3+y25    The expansion is given by the following formula :                 a+bn =…

Q: Determine the nth term formula for the number of square tiles in the nth figure. an %3D as a2 az

A: Number of tiles in a1 is 2, n=1 Number of tiles in a2 is 4, n=2 Number of tiles in a3 is 6, n=3…

Q: 24 + * ? 8 What is the coefficient for the yl8 term in the expansion of (5x°y²

A: We use the Binomial Theorem to answer the given question.

Q: The expansion of 500P3 is

A: The formula for nPr is defined as nPr = n! / (n - r)!

Q: :The nth term formula for { 1,0,1,0,... } is

A: given sequence 1, 0, 1, 0, .........

Q: find the first 4 terms of the taylor exapnsion about x 0 Ax) = 2 , Use that to approximate 2

A: From the given problem: fx=2x2.   From the Taylor series:   fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+……

Q: If in the expansion of (1 + n}+", the 5th term is 24 times the 3rd term, fnd the value of n.

A:

Q: find the fourth term in the expansion of  (x +  1   9…

A: Recall the fact that the general term of expansion ( a + b )n is as follows.

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

A: The Binomial Theorem is, (a+b)n=∑k=0nnkan-kbk Where, nk=n!k!(n-k)! The given question is to find the…

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

A: The expansion of an general expression is given by (a+b)n=∑nkan-kbkk=0n  so any term can be found…

Q: Find the 3rd term in the expansion of (5x 2)4 in simplest form.

A:

Q: What is the coefficient of x12y13 in the expansion of (2x+3y)25?

A:

Q: Find the 6th term in the expansion of (a + b)^7 in simplest form.

A:

Q: Find the coefficient of the term involving x* in the expansion of 3x – - -262444 c. -252440 а. b.…

A:

Q: Find the 2nd term in the expansion of (3x + y) in simplest form.

A:

Q: Use the Binomial theorem to find the constant term in the expansion (x -

A: To use the Binomial theorem to find the constant term in the expansion of x−1x8.

Q: Find the expansion of (x + y)4 using Binomial Theorem.

A:

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

A: Consider  (2x+1)4

Q: 22. Without expanding the power, what is the yf term in the expanded form of (x- 2y)? Show your…

A:

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

A: Given To evaluate

Q: Find the binomial expansion of √(x² +1-y²) up to the fifth term.

A: As per the question we are given a bivariate function in variables x, y and we have to find its…

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

A: The (r+1)th term of the expression (a+b)n is given by Crnan-rbr. Here C represents the combination.…

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

A:

Q: If 6th term of a G.P is 9375 and its 4th term is 375.Find its 9th term

A:

Q: Find the 2nd term in the expansion of (a + b)6 in simplest form.

A: We can find the 2nd term as below

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

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

Q: Find the 7th _term in the expansion of : 5 2x 4x

A:

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

A: Binomial theorem, (a-b)n=C0nan-C1nan-1b+C2nan-2b2-C3nan-3b3+...+Cn-1na1bn-1+Cnnbn To find binomial…

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

A: To get the term that contains y9, use the binomial expansion and obtain the second term.…