What is the sum from n=1 to infinity of n/(5^n) ?

The sum from n=1 to infinity of n/(5^n) is converges

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sum from n=1 to infinity of n/(5^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=1 to infinity of n/(5^n) ?
The sum from n=1 to infinity of n/(5^n) is converges