What is the sum from n=1 to infinity of n*(3/4)^n ?

The sum from n=1 to infinity of n*(3/4)^n is converges

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sum from n=1 to infinity of n*(3/4)^n

n = 1 \sum \infty n \cdot (\frac{3}{4})^{n}

converges

Solution steps

n = 1 \sum \infty n (\frac{3}{4})^{n}

Apply Series Ratio Test:

converges

= converges

\int \frac{9 - x ^{2}}{x ^{3}} d x

\int \frac{1}{x ^{2} 16 - x ^{2}} d x

\frac{\partial}{\partial z} (2 y^{3} z)

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

What is the sum from n=1 to infinity of n*(3/4)^n ?
The sum from n=1 to infinity of n*(3/4)^n is converges