Use differentiation to find a power series representation for f(x)=1/(1+x)^2Z

Mahagnazk

Mahagnazk

Answered question

2021-11-11

Use differentiation to find a power series representation for f(x)=1(1+x)2, What is the radius of convergence?

Answer & Explanation

Froldigh

Froldigh

Beginner2021-11-12Added 17 answers

We know that:
11+x=11(x)=n=0(x)n
If we differentiate on the interval of convergence, which is (-1,1), then we have:
f(x)=ddx[11+x]=1(1+x)2
f(x)=n=0ddx[(x)n]=n=0(1)nnxn1
1(1+x)2=n=0(1)nnxn1
1(1+x)2=n=0(1)n+1nxn1
Using Theorem 2, we know that the radius of convergence doesnt

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