What is the sum from n=0 to infinity of n(2/3)^n ?

The sum from n=0 to infinity of n(2/3)^n is converges

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sum from n=0 to infinity of n(2/3)^n

n = 0 \sum \infty n (\frac{2}{3})^{n}

converges

Solution steps

n = 0 \sum \infty n (\frac{2}{3})^{n}

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (cos (x) - x sin (x))

f (x) = x^{2} e^{- x^{2}}

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

x \cdot (1 - x)

\frac{\partial}{\partial y} (sin (x y))

What is the sum from n=0 to infinity of n(2/3)^n ?
The sum from n=0 to infinity of n(2/3)^n is converges