What is the sum from n=0 to infinity of n^2(1/2)^n ?

The sum from n=0 to infinity of n^2(1/2)^n is converges

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sum from n=0 to infinity of n^2(1/2)^n

n = 0 \sum \infty n^{2} (\frac{1}{2})^{n}

converges

Solution steps

n = 0 \sum \infty n^{2} (\frac{1}{2})^{n}

Apply Series Ratio Test:

converges

= converges

x \to 0 lim ((\frac{1}{x})^{t a n (x)})

\frac{d}{d x} (cos (x - x^{2}) (1 - 2 x))

x \to 0 lim (x^{13 x})

x \to 0 lim (\frac{1}{x} ln (1 - 2 x))

y^{^{'}} = y^{(\frac{5}{3})}

What is the sum from n=0 to infinity of n^2(1/2)^n ?
The sum from n=0 to infinity of n^2(1/2)^n is converges