What is the sum from n=0 to infinity of (n^4)/(2^n) ?

The sum from n=0 to infinity of (n^4)/(2^n) is converges

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sum from n=0 to infinity of (n^4)/(2^n)

n = 0 \sum \infty \frac{n ^{4}}{2 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{4}}{2 ^{n}}

Apply Series Ratio Test:

converges

= converges

m = 2 \sum \infty \frac{2}{5 ^{m}}

n = 1 \sum \infty \frac{1}{n ^{\frac{10}{8}}}

n = 1 \sum \infty \frac{7 n}{n !}

n = 0 \sum \infty 0. 5^{2 n}

n = 0 \sum \infty arccos (\frac{1}{n})

What is the sum from n=0 to infinity of (n^4)/(2^n) ?
The sum from n=0 to infinity of (n^4)/(2^n) is converges