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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (7 x - 1)

\frac{d}{d x} (x (x - a) ln (x + 1 + b^{2}))

\frac{d}{d x} (1 + x - y^{2})

\int \frac{x ^{n}}{n !} d x

\frac{d y}{d t} - \frac{y}{2 t} = 3 t

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