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November 23rd, 2014, 05:05 AM   #1
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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.
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November 23rd, 2014, 06:01 AM   #2
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Quote:
Originally Posted by uint View Post
I've been trying for a long time to find the sum of this. Would be nice if someone could help me!



Thanks.
$$\sum_{n=0}^{\infty}\frac{4+2^n}{4^{n+2}} =\sum_{n=0}^{\infty}\frac{4}{4^{n+2}}+\sum_{n=0}^{ \infty} \frac{2^n}{4^{n+2}}
\\ \phantom{\sum_{n=0}^{\infty}\frac{4+2^n}{4^{n+2}} } = \frac{1}{4}\sum_{n=0}^{\infty}\frac{1}{4^{n}}+ \frac{1}{16} \sum_{n=0}^{\infty} \frac{1}{2^{n}}
$$

CB
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