What is the sum from n=1 to infinity of n*2^{-n} ?

The sum from n=1 to infinity of n*2^{-n} is converges

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sum from n=1 to infinity of n*2^{-n}

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

- 5 t^{2} y^{^{''}} - 2 t y^{^{'}} + 14 y = 0

f (x) = π x

x^{2} e^{x} - 2 x e^{x} + 5 e^{x}

x \to 0 lim (\frac{x ^{2} + 5 x}{x})

x y^{^{'}} = y + x

What is the sum from n=1 to infinity of n*2^{-n} ?
The sum from n=1 to infinity of n*2^{-n} is converges