Hi there - I'm trying to work out the radius of convergence of the series [itex] \sum_{n \geq 1} n^{\sqrt{n}}z^n [/itex] and I'm not really sure where to get going - I've tried using the ratio test and got (not very far) with [itex]lim_{n \to \infty} | \frac{n^{\sqrt{n}}}{(n+1)^{\sqrt{n+1}}}|[/itex], and with the root test, [itex]\left( {lim sup_{n \to \infty} n^{\frac{1}{\sqrt{n}}}}\right) ^{-1} [/itex], neither of which seem to help me =/(adsbygoogle = window.adsbygoogle || []).push({});

I have a strong feeling the latter converges to 1 but even if I'm right I'm not totally sure how to prove it, and I may well be wrong. What should my next move be?

Thanks a lot!

Mathmos6

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# Radius of convergence help

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