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

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

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

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

converges

Solution steps

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

Apply Series Root Test:

converges

= converges

n = 3 \sum \infty \frac{4}{n ^{2} - n}

n = 0 \sum \infty \frac{1}{n ^{2} + 5 n + 4}

n = 3 \sum \infty (\frac{2}{3})^{n}

n = 1 \sum \infty \frac{1}{n ^{\frac{4}{5}}}

n = 1 \sum \infty \frac{1}{9 n ^{2} + 23}

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