What is $\displaystyle \sum_{n=0}^{\infty} (-1)^n*ln^n(2)/2$
Hello
$\displaystyle \sum_{n=0}^{\infty} (-1)^n \frac{ln^n(2)}{2}=\sum_{n=0}^{\infty} \frac{1}{2} (ln(\frac{1}{2}))^n$
Which is a convergent geometric series.
First term = $\displaystyle \frac{1}{2}$
Common ratio = $\displaystyle ln(\frac{1}{2})$
Sum = $\displaystyle \frac{\frac{1}{2}}{1-ln(\frac{1}{2})}$