- #1

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## Homework Statement

z ∈ ℂ

What is the radius of convergence of (n=0 to ∞) Σ a

_{n}z

^{n}?

## Homework Equations

I used the Cauchy-Hardamard Theorem and found the lim sup of the convergent subsequences.

[tex]a_n = \frac{n+(-1)^n}{n^2}[/tex]

lim

_{n→∞}|a

_{n}|

^{1/n}

## The Attempt at a Solution

I think that the radius of convergence is one, i.e. |z| < 1. I figured that the numerator would tend to n with the oscillating 1 and so you'd get [tex]\frac{n^{1/n}}{n^{2/n}} = 1[/tex]

R = 1/lim

_{n→∞}|a

_{n}|

^{1/n}