What is the sum from n=0 to infinity of (n^2)/(9^n) ?

The sum from n=0 to infinity of (n^2)/(9^n) is converges

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sum from n=0 to infinity of (n^2)/(9^n)

n = 0 \sum \infty \frac{n ^{2}}{9 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{2}}{9 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty n \cdot e^{- n}

n = 0 \sum \infty \frac{( - 4 ) ^{n}}{n}

n = 0 \sum \infty \frac{1}{5 ^{n} - 4 ^{n}}

n = 1 \sum \infty (cos (10))^{n}

n = 1 \sum \infty 7 n^{2} e^{- n^{3}}

What is the sum from n=0 to infinity of (n^2)/(9^n) ?
The sum from n=0 to infinity of (n^2)/(9^n) is converges