What is the sum from n=0 to infinity of (n^5)/(5^n) ?

The sum from n=0 to infinity of (n^5)/(5^n) is converges

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sum from n=0 to infinity of (n^5)/(5^n)

n = 0 \sum \infty \frac{n ^{5}}{5 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{5}}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

t \to - 1 lim (ln (t + 2))

y = \frac{z ^{2} + 1}{z ^{2} - 1}

x \to - \infty lim (\frac{x - 8}{x ^{2} + 6})

\frac{d}{d x} (\frac{d y}{d x}) + y = - 1

\int (e^{x} + e) d x

What is the sum from n=0 to infinity of (n^5)/(5^n) ?
The sum from n=0 to infinity of (n^5)/(5^n) is converges