What is the sum from n=1 to infinity of n(2/5)^n ?

The sum from n=1 to infinity of n(2/5)^n is converges

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sum from n=1 to infinity of n(2/5)^n

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty \frac{8}{5 - n}

n = 1 \sum \infty (cos (18))^{n}

n = 0 \sum \infty \frac{2 + n}{1 - 2 n}

n = 0 \sum \infty 8^{- n}

What is the sum from n=1 to infinity of n(2/5)^n ?
The sum from n=1 to infinity of n(2/5)^n is converges