What is the sum from n=1 to infinity of (n^4)/(5^n) ?

The sum from n=1 to infinity of (n^4)/(5^n) is converges

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sum from n=1 to infinity of (n^4)/(5^n)

n = 1 \sum \infty \frac{n ^{4}}{5 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{4}}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty \frac{n + 1}{2 n + 1}

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

k = 1 \sum \infty \frac{1}{( k - 1 ) ^{3}}

n = 0 \sum \infty 1 2^{n}

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

What is the sum from n=1 to infinity of (n^4)/(5^n) ?
The sum from n=1 to infinity of (n^4)/(5^n) is converges