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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{1}{n ^{2} + 10}

n = 1 \sum \infty \frac{8}{n ^{2} - 1}

k = 1 \sum \infty \frac{3}{4 ^{k}}

n = 3 \sum \infty \frac{1}{n ^{2} + 5 n}

n = 1 \sum \infty \frac{1}{n ^{3} + 4}

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