What is the sum from n=1 to infinity of ne^{-7n} ?

The sum from n=1 to infinity of ne^{-7n} is converges

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sum from n=1 to infinity of ne^{-7n}

n = 1 \sum \infty n e^{- 7 n}

converges

Solution steps

n = 1 \sum \infty n e^{- 7 n}

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (arctan^{t a n (x)} (x))

\int \frac{x}{1 + x ^{3}} d x

\frac{d}{d x} (- 8 x - cos (x))

n = 7 \sum \infty e^{5} - 2 n

\frac{d}{d x} (x^{3} x - 4)

What is the sum from n=1 to infinity of ne^{-7n} ?
The sum from n=1 to infinity of ne^{-7n} is converges