Convergence Radius: sum, k=1 to infty, {(ln k)(x-1)^k}/{k}

[johnq2k7]

Find the radius of convergence and the interval of convergence for the series listed below.

a.) sigma notation from (k=1 to infinity) of {(ln k)(x-1)^k}/{k}

i know radius of convergence is the -1/L to 1/L value for the ratio test, and the roots test can be used as well... but I need help applying it to these sigma notations ... assistance here would be greatly appreciated

please help me with this problem

 

[pka]

Re: Convergence Radius Help Needed!

On the series \(\displaystyle \sum\limits_{k = 2}^\infty {\frac{{\ln (k)\left( {x - 1} \right)^k }}{k}}\) apply the root test.
\(\displaystyle \sqrt[k]{{\left| {\frac{{\ln (k)\left( {x - 1} \right)^k }}{k}} \right|}} = \sqrt[k]{{\frac{{\ln (k)}}{k}}}\left| {\left( {x - 1} \right)} \right| \to \left| {\left( {x - 1} \right)} \right|\)