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

The sum from k=1 to infinity of (k^2)/(k!) is converges

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sum from k=1 to infinity of (k^2)/(k!)

k = 1 \sum \infty \frac{k ^{2}}{k !}

converges

Solution steps

k = 1 \sum \infty \frac{k ^{2}}{k !}

Apply Series Ratio Test:

converges

= converges

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