What is the sum from k=1 to infinity of (k^2)/(4^k) ?

The sum from k=1 to infinity of (k^2)/(4^k) is converges

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sum from k=1 to infinity of (k^2)/(4^k)

k = 1 \sum \infty \frac{k ^{2}}{4 ^{k}}

converges

Solution steps

k = 1 \sum \infty \frac{k ^{2}}{4 ^{k}}

Apply Series Ratio Test:

converges

= converges

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

n = 1 \sum \infty \frac{1}{( 2 ^{n} )}

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

n = 1 \sum \infty \frac{1}{n ^{5} + 8}

n = 0 \sum \infty cos (\frac{n}{2})

What is the sum from k=1 to infinity of (k^2)/(4^k) ?
The sum from k=1 to infinity of (k^2)/(4^k) is converges