# Decreasing series

• July 20th 2012, 11:23 AM
sander
Decreasing series
How to prove that for $a>0$ and $s_j = \sum_{i=0}^j \frac{a^i}{i!}$ the series
$f_j = \frac{s_j}{s_{j-1}}$
is decreasing?

• July 20th 2012, 10:55 PM
Prove It
Re: Decreasing series
Quote:

Originally Posted by sander
How to prove that for $a>0$ and $s_j = \sum_{i=0}^j \frac{a^i}{i!}$ the series
$f_j = \frac{s_j}{s_{j-1}}$
is decreasing?

Wouldn't \displaystyle \begin{align*} f_j \end{align*} be a sequence, not a series?
The series $\sum_{i=0}^\infty\frac{a^i}{i!}$ converges to $e^a$.