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

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

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

n = 1 \sum \infty (\frac{2}{n})^{n} \cdot n!

converges

Solution steps

n = 1 \sum \infty (\frac{2}{n})^{n} n!

Apply Series Ratio Test:

converges

= converges

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