## xEnOnn Group Title 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? 2 years ago 2 years ago

1. FoolForMath Group Title

Hint: This is a geometric series

2. satellite73 Group Title

another hint, 2>1, so convergence is unlikely

3. xEnOnn Group Title

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

4. xEnOnn Group Title

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

5. FoolForMath Group Title

How can a finite series don't converge?