What is the sum from n=1 to infinity of n(5/6)^n ?

The sum from n=1 to infinity of n(5/6)^n is converges

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sum from n=1 to infinity of n(5/6)^n

n = 1 \sum \infty n (\frac{5}{6})^{n}

converges

Solution steps

n = 1 \sum \infty n (\frac{5}{6})^{n}

Apply Series Ratio Test:

converges

= converges

n = 7 \sum \infty \frac{1}{n ^{2} - 5 n + 6}

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

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

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

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

What is the sum from n=1 to infinity of n(5/6)^n ?
The sum from n=1 to infinity of n(5/6)^n is converges