What is the sum from n=1 to infinity of (n^4)/(n!) ?

The sum from n=1 to infinity of (n^4)/(n!) is converges

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sum from n=1 to infinity of (n^4)/(n!)

n = 1 \sum \infty \frac{n ^{4}}{n !}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{4}}{n !}

Simplify

n^{4} : n^{3} n

= n = 1 \sum \infty \frac{n ^{3} n}{n !}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=1 to infinity of (n^4)/(n!) ?
The sum from n=1 to infinity of (n^4)/(n!) is converges