# Verifying a taylor series

ThatOneGuy45

## Homework Statement

For this problem I am to find the values of x in which the series converges. I know how to do that part of testing of convergence but constructing the summation part is what I am unsure about.

I am given the follwing:
1 + 2x + $\frac{3^2x^2}{2!}$ +$\frac{4^3x^3}{3!}$+ ...

## Homework Equations

I looked up online about the taylor series expansion for ex because I noticed it looked familiar and compared it with the series

The taylor series for ex is:
1 + x + $\frac{x^2}{2!}$ +$\frac{x^3}{3!}$+ ...=Ʃ$^{∞}_{n=0}$$\frac{x^n}{n!}$

## The Attempt at a Solution

What I did was pretty much just put $\frac{(n+1)^nx^n}{n!}$ and checked the terms to see if it works. It seems to work but I am just a bit unsure. I haven't worked with this stuff in a while so I just want to be sure if I did that part right.

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## Answers and Replies

clamtrox
That looks correct. You should be able to see if it converges using the ratio test, just be careful with the limit.