find the power series representation and give the interval of convergence. assume that the center of...

find the power series representation and give the interval of convergence. assume that the center of the series is a=0

g(x)= x^5 / (1+x)^3

Expert Solution

Since the given series converges for all x satisfying |x|<1 which implies - 1<x<1

Interval of convergence is (-1, 1)

Please feel free to enquire if you face any difficulty and don't hesitate to ask any question regarding this question in the comment box...

milcah answered 3 years ago

find the power series representation of each of the following functions and give an interval of...

find the power series representation of each of the following functions and give an interval of convergence for each one. assume that the center of each series is that a=0 a) xsin(x^2) b) f(x)= e^(-x^10) correction : a) f(x)=xsin (x^2)

Find the power series representation of the following functions and find the corresponding radius of convergence....

Find the power series representation of the following functions and find the corresponding radius of convergence. 1. x2(ln(5+ x)) 2. 4x/(1 + x)3

Find the sum and interval of convergence a power series I need radius of convergence or...

Find the sum and interval of convergence a power series I need radius of convergence or sum of series

Find a power series that represents the function and find the interval of convergence: a) g(x)...

Find a power series that represents the function and find the interval of convergence: a) g(x) = 1 / (3+x^2)^2 b) h(x) = ln(5 + x^2)

Determine the radius of convergence and the interval of convergence of the following power series. ∞...

Determine the radius of convergence and the interval of convergence of the following power series. ∞ ∑ n=1 (2^(1+2n))/ (((−3)^(1+2n)) n^2) (4x+2)^n .

Find the radius of convergence, R, of the series. Find the interval, I, of convergence of...

Find the radius of convergence, R, of the series. Find the interval, I, of convergence of the series. (Enter your answer using interval notation ∞ (−1)n (x − 4)n 3n + 1 n = 0 ∞ (x − 4)n n7 + 1 n = 0 ∞ 7n (x + 5)n n n = 1 ∞ (x − 13)n nn n = 1 ∞ 4nxn n2 n = 1

find the radius of convergence and interval of convergence of the series ∑ n=1 ~ ∞...

find the radius of convergence and interval of convergence of the series ∑ n=1 ~ ∞ (3^n)((x+4)^n) / √n Please solve this problem with detailed process of solving. I can't understand why the answer is [-13/3, -11/3) I thought that the answer was (-13/3, -11/3]. Can you explain why that is the answer?

Determine the interval of convergence for the power series representation of the following function. f(x)=(69x)/(4096x^6+1)

#13) Find the radius and interval of convergence of the power series (Sigma∞ n=1) (−1)^n(x −...

#13) Find the radius and interval of convergence of the power series (Sigma∞ n=1) (−1)^n(x − 1)^n/n4^n by responding to the following sequence of questions. (a) Compute the limit L = lim n→∞ |an+1|/|an| . (b) Given that the power series absolutely converges for L < 1 by the Ratio Test, compute the radius of convergence, where the radius of convergence is the real number R such that the power series converges for all |x| < R. (c) Test whether...

What is the power series representation of ln(1-2x)? What is its radius of convergence?

Question