# Math Help - Sum of an infinite series - comparing with a known series

1. ## Sum of an infinite series - comparing with a known series

Hi,

I'm doing a little revision and following through a sample exam paper.

Earlier in the current question, I found the Maclaurin Series for e^x and showed that it converges.

The last part of this question asks me to find:

sum 3^(n-1) / n!, n = 0 to infinity
Answer according to WolframAlpha

In short, I can't understand how this answer is derived. I can see x = 3 for e^x series would give me something close, but not the right answer.

It'd be great if you could offer a shove in the right direction .

Thanks in advance,
James

2. $\sum_{n=0}^{\infty} \frac{3^{n-1}}{n!}$

$=\sum_{n=0}^{\infty} \frac{3^n \cdot 3^{-1}}{n!}$

$=\frac{1}{3}\sum_{n=0}^{\infty} \frac{3^n}{n!}$

$=\frac{1}{3} \cdot e^3 = \frac{e^3}{3}$ ..

3. Thanks !