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-   -   How can I find the sum of this infinite series? (http://mymathforum.com/calculus/48044-how-can-i-find-sum-infinite-series.html)

 uint November 23rd, 2014 05:05 AM

How can I find the sum of this infinite series?

I've been trying for a long time to find the sum of this. Would be nice if someone could help me!

http://i.imgur.com/kiPutyr.png

Thanks.

 CaptainBlack November 23rd, 2014 06:01 AM

Quote:
 Originally Posted by uint (Post 213468) I've been trying for a long time to find the sum of this. Would be nice if someone could help me! http://i.imgur.com/kiPutyr.png Thanks.
$$\sum_{n=0}^{\infty}\frac{4+2^n}{4^{n+2}} =\sum_{n=0}^{\infty}\frac{4}{4^{n+2}}+\sum_{n=0}^{ \infty} \frac{2^n}{4^{n+2}} \\ \phantom{\sum_{n=0}^{\infty}\frac{4+2^n}{4^{n+2}} } = \frac{1}{4}\sum_{n=0}^{\infty}\frac{1}{4^{n}}+ \frac{1}{16} \sum_{n=0}^{\infty} \frac{1}{2^{n}}$$

CB

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