What is the sum from n=1 to infinity of (n^3)/(7^n) ?

The sum from n=1 to infinity of (n^3)/(7^n) is converges

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sum from n=1 to infinity of (n^3)/(7^n)

n = 1 \sum \infty \frac{n ^{3}}{7 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{3}}{7 ^{n}}

Apply Series Ratio Test:

converges

= converges

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\int_{0}^{\frac{π}{2}} 3 sin^{2} (3 x) d x

\int \frac{3 x ^{2} + 5}{( x ^{2} + 4 ) ^{2}} d x

What is the sum from n=1 to infinity of (n^3)/(7^n) ?
The sum from n=1 to infinity of (n^3)/(7^n) is converges