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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int_{0}^{π} (cos (x))^{6} d x

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\int \frac{- 1}{1 - 2 x + x ^{2}} d x

x \to 0 lim (e^{c s c (x)})

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