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 November 23rd, 2014, 05:05 AM #1 Member   Joined: Oct 2014 From: Norway Posts: 42 Thanks: 1 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! Thanks.
November 23rd, 2014, 06:01 AM   #2
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Quote:
 Originally Posted by uint I've been trying for a long time to find the sum of this. Would be nice if someone could help me! Thanks.
$$\sum_{n=0}^{\infty}\frac{4+2^n}{4^{n+2}} =\sum_{n=0}^{\infty}\frac{4}{4^{n+2}}+\sum_{n=0}^{ \infty} \frac{2^n}{4^{n+2}} \\ \phantom{\sum_{n=0}^{\infty}\frac{4+2^n}{4^{n+2}} } = \frac{1}{4}\sum_{n=0}^{\infty}\frac{1}{4^{n}}+ \frac{1}{16} \sum_{n=0}^{\infty} \frac{1}{2^{n}}$$

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