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

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

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

n = 1 \sum \infty e^{- n}

converges

Solution steps

n = 1 \sum \infty e^{- n}

Simplify

e^{- n} : \frac{1}{e ^{n}}

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

Apply Series Integral Test:

converges

= converges

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\frac{d}{d x} (\frac{x ^{2} + x - 2}{x - 2})

\frac{\partial}{\partial x} (ln (x^{6} - y^{4}))

f (x) = 2 (x - 3)^{2} + 1, (4, 3)

\frac{d}{d t} (cos (\frac{t ^{3}}{10}))

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