What is the sum from n=1 to infinity of n((-5)/9)^n ?

The sum from n=1 to infinity of n((-5)/9)^n is converges

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sum from n=1 to infinity of n((-5)/9)^n

n = 1 \sum \infty n (\frac{- 5}{9})^{n}

converges

Solution steps

n = 1 \sum \infty n (\frac{- 5}{9})^{n}

Simplify

= n = 1 \sum \infty n (- \frac{5}{9})^{n}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{2}{n ^{2} + 6 n}

n = 2 \sum \infty \frac{1}{n ^{1.1}}

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

n = 5 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

n = 0 \sum \infty (\frac{1}{2 - i})^{n}

What is the sum from n=1 to infinity of n((-5)/9)^n ?
The sum from n=1 to infinity of n((-5)/9)^n is converges