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

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

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

n = 0 \sum \infty e^{- n}

converges

Solution steps

n = 0 \sum \infty e^{- n}

Simplify

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

= n = 0 \sum \infty \frac{1}{e ^{n}}

Apply Series Integral Test:

converges

= converges

arctan (\frac{3 + t}{3 - t})

x \to 0 + lim (x^{7 s i n (x)})

\frac{d}{d x} (3^{4 x + 1})

x = y, 2 x + y^{2} = 8

\int_{0}^{3} \frac{1}{x x + 1} d x

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