What is the sum from n=1 to infinity of (5/n)^n ?

The sum from n=1 to infinity of (5/n)^n is converges

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sum from n=1 to infinity of (5/n)^n

n = 1 \sum \infty (\frac{5}{n})^{n}

converges

Solution steps

n = 1 \sum \infty (\frac{5}{n})^{n}

Apply Series Root Test:

converges

= converges

k = 1 \sum \infty \frac{4}{k} + 8^{- k}

n = 0 \sum \infty \frac{e ^{\frac{1}{n}}}{n}

k = 4 \sum \infty \frac{1}{k ^{2} - k}

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

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

What is the sum from n=1 to infinity of (5/n)^n ?
The sum from n=1 to infinity of (5/n)^n is converges