Analyzing the Convergence of a McLauren Series

[nns91]

Homework Statement

Given a McLauren series: (2x)^n+1 / (n+1)

(a). Find interval of convergence.

Homework Equations

Limit test

The Attempt at a Solution

So I used ratio test and found that -1/2 <x<1/2. I am testing the end point. At x=1/2, the series will be 1/(n+1) and at x=-1/2, series is (-1)^n+1 / (n+1). How do I prove whether or not they are divergent or convergent. Does 1/ (n+1) converge to 0 ?

How about when x=-1/2, is it convergent or divergent ?

 

[shaggymoods]

I imagine you forgot to put the summation notation before your terms?? McLaurin series are infinite summations; anyways, 1/(n+1) converges to 0, but this is not sufficient to prove that it converges. Can you think of a fairly famous series that this reminds you of?? Similarly for the Alternating Series at x=(-1/2); although for the alternating series you could also use the alternating series test.

 

[nns91]

Do I compare 1/(n+1) to 1/n ??