What is the sum from n=2 to infinity of (n^3)/(n!) ?

The sum from n=2 to infinity of (n^3)/(n!) is converges

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sum from n=2 to infinity of (n^3)/(n!)

n = 2 \sum \infty \frac{n ^{3}}{n !}

converges

Solution steps

n = 2 \sum \infty \frac{n ^{3}}{n !}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{9 ^{n} + n}{n !}

n = 0 \sum \infty e^{5 n}

n = 1 \sum \infty cos (n + 1)

n = 0 \sum \infty \frac{3}{2 ^{2 n}}

n = 1 \sum \infty (\frac{12}{8})^{n}

What is the sum from n=2 to infinity of (n^3)/(n!) ?
The sum from n=2 to infinity of (n^3)/(n!) is converges