Let $n$ be a natural number and let $\langle n\rangle$ denote the closest integer to $\sqrt n$. Evaluate $$\sum_{n=1}^ \infty \frac{2^{\langle n\rangle}+2^{-\langle n\rangle}}{2^n}$$ I started putting the values of $n$ to see a pattern. It looks like a Geometric Progression but I am unable to sum it. Also, if a better approach exists, please share. Thanks.
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Do you know if this problem has an analytic solution? – b00n heT Sep 09 '15 at 16:25
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The answer is $3$. If one group the terms with same $\langle n\rangle$, it is not that hard to turn this into a telescoping series. – achille hui Sep 09 '15 at 16:36
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A series is the sum of a sequence (usually countably infinite since a finite sum is just called "a sum", and uncountably infinite sets cannot have a defined sum unless all but countably many terms are zero). – hardmath Sep 09 '15 at 16:37
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Sorry, I was incorrect, this question is a duplicate, the question, process, and therefore answer are exactly the same. – Slinky Sep 09 '15 at 16:45