For which $\displaystyle x \in R$ is it convergent? $\displaystyle \sum\limits_{n=0}^\infty(-1)^n \frac{(x-2)^n}{5n9^n}$ Thank you!
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$\displaystyle \displaystyle\sqrt[n]{{\frac{{\left| {x - 2} \right|^n }}{{5n9^n }}}} \to ?<1$
First, find the radius of convergence... $\displaystyle R=\mid\frac{a_n}{a_{n+1}}\mid$ Then... $\displaystyle -R<x-2<R$ Check: $\displaystyle x=R, x=-R$
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