What is the sum from n=1 to infinity of n^2(5/8)^n ?

The sum from n=1 to infinity of n^2(5/8)^n is converges

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sum from n=1 to infinity of n^2(5/8)^n

n = 1 \sum \infty n^{2} (\frac{5}{8})^{n}

converges

Solution steps

n = 1 \sum \infty n^{2} (\frac{5}{8})^{n}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{5 ^{n}}{2 n - 1}

k = 0 \sum \infty (- \frac{5}{6})^{k}

n = 1 \sum \infty (\frac{1}{100})^{n}

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

n = 6 \sum \infty ln (\frac{n}{3})

What is the sum from n=1 to infinity of n^2(5/8)^n ?
The sum from n=1 to infinity of n^2(5/8)^n is converges