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

**sorv1986** · November 24th 2011, 01:36 AM

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

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

regards. thanx in advance.

**FernandoRevilla** · November 24th 2011, 02:31 AM

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 : $1=\limsup \sqrt[n]{2}\leq \limsup \sqrt[n]{|a_n|}\leq \limsup \sqrt[n]{3}=1$

**sorv1986** · November 24th 2011, 02:50 AM

Thanks a lot.@fernando

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