What is the sum from n=3 to infinity of n/(5^n) ?

The sum from n=3 to infinity of n/(5^n) is converges

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sum from n=3 to infinity of n/(5^n)

n = 3 \sum \infty \frac{n}{5 ^{n}}

converges

Solution steps

n = 3 \sum \infty \frac{n}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

k = 1 \sum \infty k^{\frac{1}{k}}

n = 1 \sum \infty \frac{1}{n ^{3} + 5}

n = 1 \sum \infty \frac{1}{n ^{3} - 5 n ^{2}}

k = 1 \sum \infty \frac{k ^{2}}{4 ^{k}}

n = 0 \sum \infty n 2^{n}

What is the sum from n=3 to infinity of n/(5^n) ?
The sum from n=3 to infinity of n/(5^n) is converges