18 Find the coefficient of x° in the expansion ofx -- The coefficient of x° is (Simplify your answer.)

Q: Advanced Math Determine alln >0 such that the decimal expansion of 1/n has period 1.

A: To determine all n>0 such that the decimal expansion of 1/n  has period 1.

Q: 11. Consider the expansion of 3x+ where p> 0. The coefficient of the term in x is equal to the…

A:

Q: (a) 5 Find the coefficient of x in the expansion of (2x -) . (b) Hence find the coefficient of x in…

A: You can use the binomial expansion to solve the problems as follows :

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: Sp-3 2x If there are 23 terms in the expansion of ху then the value of p is

A: We will find out the required value of p.

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

A:

Q: the coefficient of x^2n in the expansion of (1-x)^2n is

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: Q1; Vsing the Power serieg expansion for cose

A: Power series exaption for cosx

Q: For any k e Z, give a formula for the coefficient of x* in the expansion of (2-!)" 100 x²

A: Given expansion: x2-1x100 The given problem can be compared to the general form x+an. Here, n=100…

Q: 1. the largest term in the expansion of ( 1+x)^19 when x= 1/2 is ? 2. If the 2nd,3rd and 4th terms…

A: (a) As we know that from the binomial expansion, (r+1)th and rth term is given by…

Q: 5 Find the coefficient of x in the expansion of x- The coefficient of x is

A: The general term of expansion of (a+b)n  Tr+1=Crnan-rbr Here, a=x, b=-2x, n=14 So, Tr+1=Cr…

Q: z? -1 3A. Find all possible expansion of ЗА. about z = 1 z' +5z +6

A:

Q: Зх —1 A B (b) (i) Express (1– x)(2 - 3x) in the form - x 2-3x , where A and B are integers. Зх— 1…

A:

Q: (11) Use the binomial theorem and differentiation to find a formula for the sum i=0 (Hint: Consider…

A: To find: The sum ∑i=0ni-2i-1ni by using the bionomial theorem and differentiation.

Q: 12.The ratio of the coefficient of x' to the coefficient x n he expansion of (2+x)" is 12:7. The…

A: Use the binomial expension of a function and find the coefficient as asked in question than take the…

Q: (a) Expand (1+px)-S p 0 in ascending powers of x, up to and including the term in x* Give each term…

A: Ok

Q: le Find a if the 17th and 18th terms of the expansion (2 + a)" are equal.

A:

Q: 16 2 Use the binomial formula to find the coefficient of the t s term in the expansion of (t-3s)8.

A:

Q: The coefficient of xy13 in the expansion of (x + y)¹8 is O 43,758 O b 31,824 18,564 8,568 C Od

A: We know (r+1)-th term of binomial (x+y)n is  Tr+1=Crnxn-ryr

Q: 1. 1+ x +x? + x' + x* Find the coefficient of x25 in the expansion of

A: We have to find the coefficient of x25 in the expansion of 11+x+x2+x3+x4.

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

A:

Q: Q. 1 a) What is the relation between Binomial theorem and Pascal's Triangle. b) Find out the fourth…

A: Note:We are allow to answer only one question at a time. for other question please resubmit the…

Q: 3k k (3) Let n e N. Prove by mathematical induction that 4". k=0

A:

Q: 22. f (x) = e² + sin x

A: The given function is f(x)=ex+sinx .......................................... (1)

Q: b) List down the first four terms in the expansion of (1 2x) -2 in ascending power of x. Hence, by…

A:

Q: 12 Find the power of x in that term of the expansion of 2+ 2 which has the greatest numerical…

A:

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 8 cos TX ...…

A: The Maclaurin series is given by  f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: 1. Find (a +b) using the binomial theorem. 3 (a + b)' = E (3 k ) a²-kbk k=0 Show your work here:

A:

Q: 2. Consider the expansion of ( 2x + =). Assuming k is a positive constant, suppose the term 8.…

A: Soln :- (2x+kx)8 ∴ The term independent of x is 1451520 ∴ (a+b)n =∑r=0ncr arbn-rn

Q: 4. Prove that for all n E N η Σ( r=0 = = (3) Hint: Examine the coefficient of x² by expanding both…

A:

Q: 10 3. What is the coefficient of the term in the expansion of (x+y)? U. Font Family AA A EY E 三 !!!

A: Write the coefficient of the x6y4 term in the expansion of (x+y)10.

Q: 1. Find the coefficient of 2³6 in the expansion of 6 (1 +5x²5 + 12x50⁰) (x+x² + x³ + x¹ + x³ +rº +…

A:

Q: (1-x) (1+x) Find the coefficient of x" in the expansion of

A: In this problem, we have to use the expansion of (1+x)-2 and multiply the brackets to obtain the…

Q: P1. In the binomial expansion of (2-3) written in terms of descending power of X, find; a the th…

A: Explained below

Q: Q: If C,,C,, C,., C, denote the binomial coefficients in the expansion of (1+x)", prove that (-1)…

A:

Q: 7. The range of values of x for which the binomial expansion of in ascending (2+3x)(1-2x) powers of…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Consider the expansion of ( 1/ax + x2)8 . The coefficient of x7 is 56/27. Find the value of A.

A: here we can use binomial expansion to solve this question.

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

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

Q: Find the coefficient of x^0 in the expansion ((x^2)+1/x)

A: topic - binomial expansion

Q: Find the first three terms of the expansion, in ascending powers of x, of (1 – 2x)². Hence, find the…

A: Thanks for the question :)And your upvote will be really appreciable ;) First three term : -    1 ,…

Q: 2 For each of the following: i find the binomial expansion up to and including the x³ term ii state…

A: Binomial expansion…

Q: 17. The coefficient of x²y² in the expansion of (2x + 3y)4 is O 186 O 216 O 124 none of these

A:

Q: 5 (a) Consider the positive integer s = 23n-1. n=2 (i) Express s as a sum without using E-notation.…

A: Given sequence is  s=∑n=2523n-1

Q: (a) Express (4-3x) in the form of a(1+bx) where a and be R. Hence, find the expansion of (4–3x) up…

A:

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

A: Given expression is: s-2t312 We have to find the last three terms of the above expression.

Q: snip

A: The matrix A is multiplied with the matrix A itself to find a general formula. Matrix multiplication…