# How to calculate whether a series is convergent or divergent?

If a series is given for example $$1 - 1/2 + 1/4-1/8+1/16-1/32+...$$ up-to infinity how to check whether the series converges or diverges?

Is there any particular formula?

• @Vega the ratio is $-1/2$ Sep 19 at 16:07
• @Andrei oops a typo!!
– Vega
Sep 19 at 16:37

This is a geometric series, meaning the terms are of form $$a, ar, ar^2, ...$$ In your particular case $$a=1$$ and $$r=-1/2$$. This series is convergent if $$|r|<1$$. The link provided also shows you that the sum is $$\sum_{k=0}^\infty ar^k=\frac a{1-r}$$
• This is right if we assume that the sequence in OP follows the pattern. But nothing tells us what there is after $-1/32$, so the question is not well posed Sep 19 at 16:14