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How to find the center of the power series.

$\sum _{ n=0 }^{ \infty }{ \frac { 2n(x+1)^ n }{ 3^ n } } $

I think it to be (x-(-1))= so, the center is -1

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By definition a power series $\Sigma a_n(x-x_0)^n$ is centered at $x_0$. So in your problem it's indeed centered at -1

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