what is the radius of convergence of the power series Σan xⁿ

• December 27th 2011, 06:18 AM
sorv1986
what is the radius of convergence of the power series Σan xⁿ
suppose Σan xⁿ be a power series and an= the number of divisors of n⁵⁰.

Then what will be the radius of convergence of this power series?

• December 27th 2011, 07:15 AM
FernandoRevilla
Re: what is the radius of convergence of the power series Σan xⁿ
Quote:

Originally Posted by sorv1986
suppose Σan xⁿ be a power series and an= the number of divisors of n⁵⁰. Then what will be the radius of convergence of this power series?

Hint $1\leq a_n\leq n^{50}\Rightarrow 1\leq a_n^{1/n}\leq (n^{1/n})^{50}$ . Now, apply the Sandwich Theorem.