What is the sum from n=0 to infinity of (n+1)0.5^n ?

The sum from n=0 to infinity of (n+1)0.5^n is converges

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sum from n=0 to infinity of (n+1)0.5^n

n = 0 \sum \infty (n + 1) 0. 5^{n}

converges

Solution steps

n = 0 \sum \infty (n + 1) \cdot 0. 5^{n}

Apply Series Ratio Test:

converges

= converges

sin (x + sin (4 x))

y^{^{'}} = (1 - 2 x) y^{2}

n = 1 \sum \infty \frac{1 5 ^{n}}{n !}

\frac{d}{d x} (4 x e^{2 x})

\frac{d}{d x} (x, y)

What is the sum from n=0 to infinity of (n+1)0.5^n ?
The sum from n=0 to infinity of (n+1)0.5^n is converges