What is the sum from n=0 to infinity of (n^2)/(7^n) ?

The sum from n=0 to infinity of (n^2)/(7^n) is converges

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sum from n=0 to infinity of (n^2)/(7^n)

n = 0 \sum \infty \frac{n ^{2}}{7 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{2}}{7 ^{n}}

Apply Series Ratio Test:

converges

= converges

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

n = 1 \sum \infty \frac{8}{e ^{n} - 1}

n = 0 \sum \infty \frac{1}{2 n ^{3}}

n = 0 \sum \infty \frac{n}{( n + 1 ) ^{2}}

n = 0 \sum \infty \frac{n + 1}{3 n + 1}

What is the sum from n=0 to infinity of (n^2)/(7^n) ?
The sum from n=0 to infinity of (n^2)/(7^n) is converges