## anonymous 4 years ago How can I know what a summation of series will eventually converge to? For example, in this series: $\sum _{ i=1 }^{ n }{ { 2 }^{ i-1 } }$ What are the steps I should take to know that it will eventually converge into what equation?

1. anonymous

Hint: This is a geometric series

2. anonymous

another hint, 2>1, so convergence is unlikely

3. anonymous

Thanks for the hints. By the way, it does converge. It converges to $2^n-1$

4. anonymous

But of course, if the series goes to infinity, then it wouldn't converge.

5. anonymous

How can a finite series don't converge?