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Let $\sum a_n x^n$ be a power series with radius of convergence $R$.

What is the radius of convergence of $\sum a_n x^{n^2}$?

Can anyone help me here?

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    $\begingroup$ Do you know the formula with $\limsup |a_n|^{1/n}$? Use it for the second series. The indices with zero coefficients can be ignored for the computations of $\limsup$ $\endgroup$ – user147263 Oct 26 '14 at 18:16
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Hint: Let $b_k:=a_n$ if $k=n^2$ and $b_k:=0$ else.

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  • $\begingroup$ and now i use weierstrass test? $\endgroup$ – user187492 Oct 26 '14 at 18:11
  • $\begingroup$ Well, I thought about the formula with $\limsup$, commented by @WeaponofChoice. $\endgroup$ – Berci Oct 26 '14 at 18:31

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