# Infinite series

1. Apr 27, 2010

i'm going through a proof and i cant seem to workout why this equality makes sense
$$\sum^{10^{i}-1}_{k=0} \frac{k}{10^i} = \frac{(10^i-1)}{2}$$
this may be obvious, any hints atleast would be much appreciated

2. Apr 27, 2010

### NaturePaper

This is just $$\sum\limits_{k=0}^{n-1}k=\frac{n(n-1)}{2}$$; in your problem, replace $$n \mbox{ by } 10^i$$.

By the way, your series is a finite one :)
Cheers.

Last edited: Apr 27, 2010