What is the sum from n=1 to infinity of ne^{-15n} ?

The sum from n=1 to infinity of ne^{-15n} is converges

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sum from n=1 to infinity of ne^{-15n}

n = 1 \sum \infty n e^{- 15 n}

converges

Solution steps

n = 1 \sum \infty n e^{- 15 n}

Apply Series Ratio Test:

converges

= converges

n = 2 \sum \infty \frac{5}{n ^{2} - 1}

n = 1 \sum \infty \frac{1}{n ^{\frac{9}{8}}}

n = 1 \sum \infty \frac{5}{n ^{e}}

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

n = 1 \sum \infty \frac{5 ^{n}}{7 ^{n}}

What is the sum from n=1 to infinity of ne^{-15n} ?
The sum from n=1 to infinity of ne^{-15n} is converges