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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

k = 3 \sum \infty \frac{1}{( k - 2 ) ^{3}}

n = 0 \sum \infty \frac{i ^{2 n}}{2 n}

k = 1 \sum \infty \frac{1}{k k}

n = 0 \sum \infty 7 + \frac{5}{n ^{5}}

n = 1 \sum \infty (1.05)^{n}

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