What is the sum from n=1 to infinity of n^2(1/3)^n ?

The sum from n=1 to infinity of n^2(1/3)^n is converges

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sum from n=1 to infinity of n^2(1/3)^n

n = 1 \sum \infty n^{2} (\frac{1}{3})^{n}

converges

Solution steps

n = 1 \sum \infty n^{2} (\frac{1}{3})^{n}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=1 to infinity of n^2(1/3)^n ?
The sum from n=1 to infinity of n^2(1/3)^n is converges