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

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

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

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

converges

Solution steps

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

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

L > 1,

by the Raabe's test

= converges

6^{s i n (π x)}

\int_{0}^{\infty} t e^{- t} d t

\frac{x}{x ^{2} + 49}

t \to 2 lim (\frac{t ^{2} - 4}{t - 2})

x^{^{'}} + 4 x = t e^{- 4 t}

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