What is the sum from n=1 to infinity of ne^{-n/2} ?

The sum from n=1 to infinity of ne^{-n/2} is converges

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sum from n=1 to infinity of ne^{-n/2}

n = 1 \sum \infty n e^{- \frac{n}{2}}

converges

Solution steps

n = 1 \sum \infty n e^{- \frac{n}{2}}

Apply Series Ratio Test:

converges

= converges

\int \frac{4 x + 2}{x ^{2}} d x

\frac{d}{d x} (arccot (e^{x}))

\int \frac{3 x ^{2}}{x ^{2} - 1} d x

\frac{d}{d x} (- 3 a sin (3 x) + 3 b cos (3 x))

x \to 5 + lim (\frac{2 x}{x - 5})

What is the sum from n=1 to infinity of ne^{-n/2} ?
The sum from n=1 to infinity of ne^{-n/2} is converges