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

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

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

n = 0 \sum \infty \frac{n}{4 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n}{4 ^{n}}

Apply Series Ratio Test:

converges

= converges

\int sin (6 x) cos (4 x) d x

\int x^{3} d x

\frac{d}{d x} (- 4 x^{2} + 2 x - 3)

- 2 x^{4} (4 x^{2} + 1)^{3}

t \to 0 lim (\frac{e ^{2 t}}{sin ( t )})

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