What is the sum from n=0 to infinity of (n^3)/(4^n) ?

The sum from n=0 to infinity of (n^3)/(4^n) is converges

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sum from n=0 to infinity of (n^3)/(4^n)

n = 0 \sum \infty \frac{n ^{3}}{4 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{3}}{4 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 5 \sum \infty \frac{n + 1}{n ^{3}}

n = 0 \sum \infty \frac{1}{2 - n}

n = 0 \sum \infty (\frac{5}{7})^{n}

n = 1 \sum \infty \frac{n !}{9 ^{n}}

k = 1 \sum \infty \frac{4}{k} - \frac{4}{k + 1}

What is the sum from n=0 to infinity of (n^3)/(4^n) ?
The sum from n=0 to infinity of (n^3)/(4^n) is converges