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

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

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

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

converges

Solution steps

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

Simplify

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

Apply Series Ratio Test:

converges

= converges

(x + y) d x + (x) d y = 0

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\frac{d y}{d x} = (cos (2 x))

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = - 5, y^{^{'}} (0) = - 1

\int (2 y sin (x) + e^{2 z}) d y

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