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Is there a solution for the infinite sum of the following form??

$x^y + x^{y + y^2} + x^{y + y^2 + y^3} + x^{y + y^2 + y^3 + y^4} + ...$

It can also be represented this way:

$\sum_{j = 1}^{\infty} \prod_{k = 1}^{j} x^{y^k}$

Any tips would be greatly appreciated-- both me and Wolfram Alpha are stumped on this one!

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Another possible representation: $x^{\frac{y}{1 - y}} \left [ \sum_{j = 2}^{\infty} x^{\frac{-y^j}{1 - y}} \right ]$ – Matt D. Dec 28 '13 at 15:39
Wait, actually I think the sum is infinite. So, answer away for easy points! – Matt D. Dec 28 '13 at 15:55
It depends - if $x=1/2$ and $y\gt 1$, it certainly converges. – Ian Mateus Dec 28 '13 at 15:56

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