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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int x^{2} - 4 d x

\frac{d}{d x} ((x - 3) \cdot ln (\frac{x}{3}))

\frac{d}{d x} (\frac{2 - x}{x ^{2}})

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

x \to 1 - lim (2^{\frac{1}{x - 1}})

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