What is the sum from n=0 to infinity of n^2e^{-7n} ?

The sum from n=0 to infinity of n^2e^{-7n} is converges

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sum from n=0 to infinity of n^2e^{-7n}

n = 0 \sum \infty n^{2} e^{- 7 n}

converges

Solution steps

n = 0 \sum \infty n^{2} e^{- 7 n}

Apply Series Ratio Test:

converges

= converges

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\frac{5}{s ( 4 s ^{2} + 4 s + 1 )}

What is the sum from n=0 to infinity of n^2e^{-7n} ?
The sum from n=0 to infinity of n^2e^{-7n} is converges