What is the sum from n=1 to infinity of n(8/9)^n ?

The sum from n=1 to infinity of n(8/9)^n is converges

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sum from n=1 to infinity of n(8/9)^n

n = 1 \sum \infty n (\frac{8}{9})^{n}

converges

Solution steps

n = 1 \sum \infty n (\frac{8}{9})^{n}

Apply Series Ratio Test:

converges

= converges

k = 1 \sum \infty \frac{1}{k} - \frac{1}{k + 2}

n = 1 \sum \infty 6 ln (\frac{n}{n + 1})

k = 0 \sum \infty \frac{k}{2 k + 1}

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

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

What is the sum from n=1 to infinity of n(8/9)^n ?
The sum from n=1 to infinity of n(8/9)^n is converges