What is the sum from n=0 to infinity of e^{-10n} ?

The sum from n=0 to infinity of e^{-10n} is converges

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sum from n=0 to infinity of e^{-10n}

n = 0 \sum \infty e^{- 10 n}

converges

Solution steps

n = 0 \sum \infty e^{- 10 n}

Apply Series Integral Test:

converges

= converges

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

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

n = 1 \sum \infty \frac{6 ^{n}}{n + 1}

n = 1 \sum \infty cos (\frac{7}{n})

n = 0 \sum \infty \frac{1}{4 + 3 n}

What is the sum from n=0 to infinity of e^{-10n} ?
The sum from n=0 to infinity of e^{-10n} is converges