# Math Help - Finding the Sum of an Infinite Series

1. ## Finding the Sum of an Infinite Series

http://www-users.math.umd.edu/~wojte...d_3_sample.pdf

It's #2.

Note: This is only a sample exam.

2. We have:

$\displaystyle\sum_{k=1}^{\infty}\dfrac{(-1)^k4^{k-1}}{3^{2k}}}=\dfrac{1}{4}\displaystyle\sum_{k=1}^{ \infty}\left(\frac{-4}{9}\right)^k=\ldots$

Now, use a well known theorem about geometric series.

Regards.

Fernando Revilla

3. @Fernando: Thanks! I'm not the best at manipulating series :P

4. Originally Posted by kgarcia3
@Fernando: Thanks! I'm not the best at manipulating series :P
Neither do I.

Regards.

Fernando Revilla