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?

  • $\begingroup$ @Vega the ratio is $-1/2$ $\endgroup$
    – Andrei
    Sep 19 at 16:07
  • $\begingroup$ @Andrei oops a typo!! $\endgroup$
    – 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 $$\sum_{k=0}^\infty ar^k=\frac a{1-r}$$

  • 1
    $\begingroup$ 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 $\endgroup$
    – Snoop
    Sep 19 at 16:14

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