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

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

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

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

converges

Solution steps

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

Apply Series Integral Test:

converges

= converges

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\frac{d y}{d x} = \frac{( 2 x ( y - 1 ) )}{x ^{2} + 3}

\int \frac{1}{x ^{2} 16 + x ^{2}} d x

\int \frac{x}{x - 3} d x

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