What is the sum from n=0 to infinity of (n^6)/(2^n) ?

The sum from n=0 to infinity of (n^6)/(2^n) is converges

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sum from n=0 to infinity of (n^6)/(2^n)

n = 0 \sum \infty \frac{n ^{6}}{2 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{6}}{2 ^{n}}

Apply Series Ratio Test:

converges

= converges

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

\frac{d}{d x} (\frac{2 x ^{3} - 7}{x ^{2}})

y = 3 x^{2} - x^{3}, (1, 2)

\int (8 cos (x) + 9 sin (x)) d x

\int - \frac{1}{4} csc (8 t) d t

What is the sum from n=0 to infinity of (n^6)/(2^n) ?
The sum from n=0 to infinity of (n^6)/(2^n) is converges