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## Homework Statement

Find the interval of convergence.

## Homework Equations

[itex]\displaystyle \sum^{∞}_{n=0} \frac{(x-5)^n}{n^4 * 2^n}[/itex]

## The Attempt at a Solution

I used the ratio test as follows:

[itex]\displaystyle \frac{(x-5)^{n+1}}{(n+1)^4 * 2^{n+1}} * \frac{n^4 2^n}{(x-5)^n}[/itex]

taking the limit:

(x-5) lim (x->inf) [itex]\displaystyle \frac{n^4}{2(n+1)^4}[/itex] = 0

Most of these problems the limit comes to 1. How do i solve this now that the limit is zero?