# Homework Help: Use ratio test to find radius and interval of convergence of power series

1. Oct 30, 2012

### marylou

1. The problem statement, all variables and given/known data

Use the ratio test to find the radius of convergence and the interval of convergence of the power series:

[[Shown in attachment]]

2. Relevant equations

an+1/an=k

Interval of convergence: | x-a |∠ R

3. The attempt at a solution

I began by finding the summation which I concluded was:

Ʃ (2^n)(x-0)^n / n(factorial)

So an+1/an = [2n+1/(n+1)(factorial)] *times* [ n(factorial)/ 2n ]

After cancelling, I arrived at 2/(n+1)

If that lim n→∞ is taken, it would be 0, meaning the radius of convergence is ∞, and the interval is from -∞ to ∞. Is that true or did I make a mistake, because the website for my homework won't allow me to enter infinity (∞)?

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2. Oct 30, 2012

### Staff: Mentor

What happened to x?

BTW, the symbol for factorial is !, so you can write n! instead of n factorial.