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 \frac{n}{( - 2 ) ^{n}}

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty \frac{4}{5 n}

n = 1 \sum \infty n - 2

n = 3 \sum \infty \frac{6}{( n ^{2} - 1 )}

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

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

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