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

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

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

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

converges

Solution steps

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{n ^{n}} = n^{- n}

= n = 2 \sum \infty n^{- n}

Apply Series Root Test:

converges

= converges

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