What is the sum from k=1 to infinity of e^{-k^2} ?

The sum from k=1 to infinity of e^{-k^2} is converges

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sum from k=1 to infinity of e^{-k^2}

k = 1 \sum \infty e^{- k^{2}}

converges

Solution steps

k = 1 \sum \infty e^{- k^{2}}

Apply Series Ratio Test:

converges

= converges

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What is the sum from k=1 to infinity of e^{-k^2} ?
The sum from k=1 to infinity of e^{-k^2} is converges