What is the sum from n=0 to infinity of n(1/4)^n ?

The sum from n=0 to infinity of n(1/4)^n is converges

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sum from n=0 to infinity of n(1/4)^n

n = 0 \sum \infty n (\frac{1}{4})^{n}

converges

Solution steps

n = 0 \sum \infty n (\frac{1}{4})^{n}

Apply Series Root Test:

converges

= converges

\int \frac{e ^{x}}{3 + 5 e ^{2 x}} d x

\frac{d}{d t} (cos (π t))

\frac{\partial}{\partial x} (x^{3} - 3 x y^{2} + y^{3})

n = 1 \sum \infty \frac{7}{n} - \frac{7}{n + 1}

x \to 0 lim (- 6 + 6 x^{3})

What is the sum from n=0 to infinity of n(1/4)^n ?
The sum from n=0 to infinity of n(1/4)^n is converges