How-do-you-solve-the-following-series-i-0-1-i-1-2-i-1-

Question Number 2181 by Filup last updated on 07/Nov/15

How do you solve the following series ?

\underset{i = 0}{\sum^{\infty}} {(- 1)}^{i} \frac{1}{2 (i + 1)}

Answered by prakash jain last updated on 08/Nov/15

\underset{i = 0}{\sum^{\infty}} {(- 1)}^{i} \frac{1}{i + 1} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + . . = \ln 2

Commented by Filup last updated on 07/Nov/15

Is there a simple way to show where

this answer comes from ? A proof ?

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