What is the sum from n=1 to infinity of (n^6)/(6^n) ?

The sum from n=1 to infinity of (n^6)/(6^n) is converges

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sum from n=1 to infinity of (n^6)/(6^n)

n = 1 \sum \infty \frac{n ^{6}}{6 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{6}}{6 ^{n}}

Apply Series Ratio Test:

converges

= converges

\int \frac{w}{w ^{3} + w ^{2} + 4 w + 4} d w

\int e^{- 3 x} sin (x) d x

\int_{- 2}^{1} \frac{1}{x + 3} d x

x \to 0 + lim (\frac{x ^{2}}{7} - \frac{2}{x})

x \to 0 lim ((1 + 3 x)^{\frac{2}{3}})

What is the sum from n=1 to infinity of (n^6)/(6^n) ?
The sum from n=1 to infinity of (n^6)/(6^n) is converges