What is the sum from n=0 to infinity of e^{-(3n)/2} ?

The sum from n=0 to infinity of e^{-(3n)/2} is converges

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sum from n=0 to infinity of e^{-(3n)/2}

n = 0 \sum \infty e^{- \frac{3 n}{2}}

converges

Solution steps

n = 0 \sum \infty e^{- \frac{3 n}{2}}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of e^{-(3n)/2} ?
The sum from n=0 to infinity of e^{-(3n)/2} is converges