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$$\sum_{i=0}^k 2^{n/{2^i}}$$

I'm trying to find an actual sum of this little nice sum , but I think that there's a problem

with it being a geometric series .

I'd appreciate any help


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Try calculating the $log$ of this expression. – ofer Apr 14 '12 at 7:21
@ofer: The $log$ ? but I do not need the $log$ of this expression , or do I ? – ron Apr 14 '12 at 7:34
It is not a geometric series. If $x=2^n$, you are looking at $x+\sqrt{x}+\sqrt[4]{x}+\sqrt[8]{x}+\cdots$ (finite sum). No pleasant closed form. – André Nicolas Apr 14 '12 at 7:38
@AndréNicolas: Then what you're saying is that I can't find its final sum ? – ron Apr 14 '12 at 7:55
@ron: I am at least saying that I cannot! Also, there will not be a closed form in terms of standard functions. – André Nicolas Apr 14 '12 at 7:58

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