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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\frac{d}{d x} ((4 x^{2} + 1)^{- 50})

\int (\frac{x ^{2} + 3 x - 5}{x - 3}) d x

\int 2 + x^{2} d x

\frac{d}{d x} (\frac{y}{3 x})

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