What is the sum from n=1 to infinity of 5^{-3n} ?

The sum from n=1 to infinity of 5^{-3n} is converges

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sum from n=1 to infinity of 5^{-3n}

n = 1 \sum \infty 5^{- 3 n}

converges

Solution steps

n = 1 \sum \infty 5^{- 3 n}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{1}{e ^{4 n}}

n = 2 \sum \infty (- 0.55)^{n}

n = 1 \sum \infty \frac{2}{n ^{3} + 4}

n = 1 \sum \infty \frac{2 n}{3 n + 6}

n = 0 \sum \infty \frac{n}{6 ^{n}}

What is the sum from n=1 to infinity of 5^{-3n} ?
The sum from n=1 to infinity of 5^{-3n} is converges