# alternating series

• Apr 26th 2010, 10:01 PM
Brotha
alternating series
sum_(n=-1)^infinity(-1)^(n+1) (1/3)^n = 9/4~~2.25...

How do you prove that? Is there a certain formula to figure out the sum of the alternating series?
• Apr 26th 2010, 10:37 PM
Chris L T521
Quote:

Originally Posted by Brotha
sum_(n=-1)^infinity(-1)^(n+1) (1/3)^n = 9/4~~2.25...

How do you prove that? Is there a certain formula to figure out the sum of the alternating series?

It appears to be geometric in form. Observe that:

$\sum_{n=-1}^{\infty}(-1)^{n+1}\left(\tfrac{1}{3}\right)^n=3-\sum_{n=0}^{\infty}\left(-\tfrac{1}{3}\right)^n=\ldots$

Can you finish this?