# Thread: Decreasing series

1. ## 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?

Thanks in advance!

2. ## Re: Decreasing series

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?

Thanks in advance!
Wouldn't \displaystyle \begin{align*} f_j \end{align*} be a sequence, not a series?

3. ## Re: Decreasing series

The series $\sum_{i=0}^\infty\frac{a^i}{i!}$ converges to $e^a$.