Math Help - Simple Sum

1. Simple Sum

What is $\sum_{n=0}^{\infty} (-1)^n*ln^n(2)/2$

2. Originally Posted by PaulDirac2
What is $\sum_{n=0}^{\infty} (-1)^n*ln^n(2)/2$
Hello

$\sum_{n=0}^{\infty} (-1)^n \frac{ln^n(2)}{2}=\sum_{n=0}^{\infty} \frac{1}{2} (ln(\frac{1}{2}))^n$

Which is a convergent geometric series.
First term = $\frac{1}{2}$
Common ratio = $ln(\frac{1}{2})$
Sum = $\frac{\frac{1}{2}}{1-ln(\frac{1}{2})}$

3. Thanks

Thanks you for helping.