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

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

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

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

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

\int_{2}^{3} 20 x d x

f (x) = x^{2} - 4, g (x) = 0

\frac{1}{2} (2 - x^{2})^{- \frac{1}{2}}

\frac{\partial}{\partial x} (e^{2 x} cos (x^{2} y))

x \to - 5 + lim (\frac{2}{x ^{2} - 25})

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