What is the sum from n=1 to infinity of n*(4/5)^n ?

The sum from n=1 to infinity of n*(4/5)^n is converges

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sum from n=1 to infinity of n*(4/5)^n

n = 1 \sum \infty n \cdot (\frac{4}{5})^{n}

converges

Solution steps

n = 1 \sum \infty n (\frac{4}{5})^{n}

Apply Series Ratio Test:

converges

= converges

x \to 0 + lim (x (ln (x)))

4 x^{2} - 3 x + 2

\int_{1}^{3} x^{4} d x

f^{^{'}} (x) = 2 x + 3 x^{1.7}

\frac{d}{d x} (\frac{1}{x ( ln ( x ) ) ^{\frac{2}{3}}})

What is the sum from n=1 to infinity of n*(4/5)^n ?
The sum from n=1 to infinity of n*(4/5)^n is converges