# Thread: what is the radius of convergence of the power series when an is given as

1. ## what is the radius of convergence of the power series when an is given as

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

a0=1, ,2<= |an| <= 3 for all n>=1 ?

2. ## Re: what is the radius of convergence of the power series when an is given as

Originally Posted by sorv1986
what is the radius of convergence of the power series Σan xⁿ, where a0=1, ,2<= |an| <= 3 for all n>=1 ?
Hint : $1=\limsup \sqrt[n]{2}\leq \limsup \sqrt[n]{|a_n|}\leq \limsup \sqrt[n]{3}=1$

3. ## Re: what is the radius of convergence of the power series when an is given as

Thanks a lot.@fernando