What is the sum from n=1 to infinity of e^{-n/6} ?

The sum from n=1 to infinity of e^{-n/6} is converges

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sum from n=1 to infinity of e^{-n/6}

n = 1 \sum \infty e^{- \frac{n}{6}}

converges

Solution steps

n = 1 \sum \infty e^{- \frac{n}{6}}

Apply Series Ratio Test:

converges

= converges

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

n = 4 \sum \infty \frac{2}{5 n ^{3}}

n = 0 \sum \infty 1 + \frac{( - 1 ) ^{n}}{n}

k = 1 \sum \infty [(k) (\frac{1}{2})^{k}]

n = 2 \sum \infty \frac{n ^{n}}{n !}

What is the sum from n=1 to infinity of e^{-n/6} ?
The sum from n=1 to infinity of e^{-n/6} is converges