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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int_{x^{2}}^{4 - x^{2}} y d y

\int \frac{1}{( x ^{2} + 4 ) ^{\frac{5}{2}}} d x

y = 2 x e^{- 3 x} + 3 e^{x^{2}}

y^{^{''}} = 3 t^{2}

\int e^{(- s t)} d t

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