What is the sum from n=0 to infinity of 1e^{-5n} ?

The sum from n=0 to infinity of 1e^{-5n} is converges

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sum from n=0 to infinity of 1e^{-5n}

n = 0 \sum \infty 1 e^{- 5 n}

converges

Solution steps

n = 0 \sum \infty 1 \cdot e^{- 5 n}

Simplify

= n = 0 \sum \infty e^{- 5 n}

Apply Series Integral Test:

converges

= converges

n = 0 \sum \infty (\frac{8}{5})^{n}

k = 2 \sum \infty (- 0.5)^{k}

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

n = 0 \sum \infty n^{4}

n = 0 \sum \infty n^{9}

What is the sum from n=0 to infinity of 1e^{-5n} ?
The sum from n=0 to infinity of 1e^{-5n} is converges