What is the sum from n=1 to infinity of (n^4)/(8^n) ?

The sum from n=1 to infinity of (n^4)/(8^n) is converges

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sum from n=1 to infinity of (n^4)/(8^n)

n = 1 \sum \infty \frac{n ^{4}}{8 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{4}}{8 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{n}{n ^{2} + 16}

k = 1 \sum \infty (\frac{π}{e})^{- k}

n = 1 \sum \infty \frac{n}{cos ( n )}

n = 1 \sum \infty \frac{1}{n ^{2} - 4 n + 5}

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

What is the sum from n=1 to infinity of (n^4)/(8^n) ?
The sum from n=1 to infinity of (n^4)/(8^n) is converges