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?

Question

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?

anonymous · Answer

Hint: This is a geometric series

anonymous · Answer

another hint,
2>1, so convergence is unlikely

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

How can a finite series don't converge?