What is the sum from n=1 to infinity of n*0.5^n ?

The sum from n=1 to infinity of n*0.5^n is converges

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sum from n=1 to infinity of n*0.5^n

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1.3 \sum \infty e^{- 1.8 n}

n = 1 \sum \infty \frac{1}{( 4 n ) ^{5}}

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

n = 1 \sum \infty \frac{ln ( 8 n )}{n}

k = 0 \sum \infty 9 \cdot (\frac{3}{5})^{k}

What is the sum from n=1 to infinity of n*0.5^n ?
The sum from n=1 to infinity of n*0.5^n is converges