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?

  • 1
    $\begingroup$ 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

Hint: Let $b_k:=a_n$ if $k=n^2$ and $b_k:=0$ else.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.