What is the sum from n=1 to infinity of n(2/3)^n ?

The sum from n=1 to infinity of n(2/3)^n is converges

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sum from n=1 to infinity of n(2/3)^n

n = 1 \sum \infty n (\frac{2}{3})^{n}

converges

Solution steps

n = 1 \sum \infty n (\frac{2}{3})^{n}

Apply Series Ratio Test:

converges

= converges

y = sin (x), y = x, x = \frac{π}{2}, x = π

3 + 5 sin (x)

\int_{0}^{a} 7 x a^{2} - x^{2} d x

\frac{a x}{x ^{2} + a ^{2}}

\frac{d y}{d x} + 2 x y = - x y^{4}

What is the sum from n=1 to infinity of n(2/3)^n ?
The sum from n=1 to infinity of n(2/3)^n is converges