What is the sum from n=2 to infinity of (5/6)^{3n} ?

The sum from n=2 to infinity of (5/6)^{3n} is converges

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sum from n=2 to infinity of (5/6)^{3n}

n = 2 \sum \infty (\frac{5}{6})^{3 n}

converges

Solution steps

n = 2 \sum \infty (\frac{5}{6})^{3 n}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{1 8 ^{n}}{n !}

k = 0 \sum \infty (\frac{k}{k + 15})^{k}

k = 1 \sum \infty \frac{1}{k ^{6}}

k = 0 \sum \infty (0.8)^{k}

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

What is the sum from n=2 to infinity of (5/6)^{3n} ?
The sum from n=2 to infinity of (5/6)^{3n} is converges