What is the sum from n=0 to infinity of n(3/5)^n ?

The sum from n=0 to infinity of n(3/5)^n is converges

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sum from n=0 to infinity of n(3/5)^n

n = 0 \sum \infty n (\frac{3}{5})^{n}

converges

Solution steps

n = 0 \sum \infty n (\frac{3}{5})^{n}

Apply Series Ratio Test:

converges

= converges

25 x^{2} y^{^{''}} + 25 x y^{^{'}} + y = 0

x \to \infty lim (x^{x})

d er i v a t i v e \frac{- 8 x - 2}{9 x - 4}

\frac{\partial}{\partial x} (4 x^{3} + y)

d er i v a t i v e \frac{10 x + 1}{x + 100}

What is the sum from n=0 to infinity of n(3/5)^n ?
The sum from n=0 to infinity of n(3/5)^n is converges