What is the sum from n=0 to infinity of n(3/4)^n ?

The sum from n=0 to infinity of n(3/4)^n is converges

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sum from n=0 to infinity of n(3/4)^n

n = 0 \sum \infty n (\frac{3}{4})^{n}

converges

Solution steps

n = 0 \sum \infty n (\frac{3}{4})^{n}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of n(3/4)^n ?
The sum from n=0 to infinity of n(3/4)^n is converges