What is the sum from n=0 to infinity of e^{-2nab} ?

The sum from n=0 to infinity of e^{-2nab} is converges

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sum from n=0 to infinity of e^{-2nab}

n = 0 \sum \infty e^{- 2 nab}

converges

Solution steps

n = 0 \sum \infty e^{- 2 nab}

n \to \infty lim (n (\frac{e ^{- 2 nab}}{e ^{- 2 (n + 1) ab}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

n = 1 \sum \infty \frac{1}{3 n + 5}

\int \frac{1}{y - x} d x

n = 1 \sum \infty \frac{1}{n ^{2} + 5 n}

x \to - 4 lim (x^{2} - 16)

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

What is the sum from n=0 to infinity of e^{-2nab} ?
The sum from n=0 to infinity of e^{-2nab} is converges