What is the sum from n=1 to infinity of 1/(n+1^{-n)} ?

The sum from n=1 to infinity of 1/(n+1^{-n)} is diverges

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sum from n=1 to infinity of 1/(n+1^{-n)}

n = 1 \sum \infty \frac{1}{n + 1 ^{- n}}

diverges

Solution steps

n = 1 \sum \infty \frac{1}{n + 1 ^{- n}}

Simplify

= n = 1 \sum \infty \frac{1}{n + 1}

Apply Series Limit Comparison Test:

diverges

= diverges

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What is the sum from n=1 to infinity of 1/(n+1^{-n)} ?
The sum from n=1 to infinity of 1/(n+1^{-n)} is diverges