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

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

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

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

converges

Solution steps

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

n \to \infty lim (n (\frac{e ^{- an}}{e ^{- a (n + 1)}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

\frac{2 d y}{d x} + 6 y = 3

x \to \infty lim (- 12)

\frac{d}{d x} (- \frac{4 x - 3}{( 2 x ^{2} - 3 x + 1 ) ^{2}})

\int_{- 5}^{5} 4 + ∣ x ∣ d x

x \to 3 + lim (x - 1)

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