What is the sum from n=0 to infinity of (n+1)e^{-n} ?

The sum from n=0 to infinity of (n+1)e^{-n} is converges

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sum from n=0 to infinity of (n+1)e^{-n}

n = 0 \sum \infty (n + 1) e^{- n}

converges

Solution steps

n = 0 \sum \infty (n + 1) e^{- n}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of (n+1)e^{-n} ?
The sum from n=0 to infinity of (n+1)e^{-n} is converges