What is the sum from n=0 to infinity of e^{(-9n)/2} ?

The sum from n=0 to infinity of e^{(-9n)/2} is converges

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sum from n=0 to infinity of e^{(-9n)/2}

n = 0 \sum \infty e^{\frac{- 9 n}{2}}

converges

Solution steps

n = 0 \sum \infty e^{\frac{- 9 n}{2}}

Simplify

= n = 0 \sum \infty e^{- \frac{9 n}{2}}

Apply Series Ratio Test:

converges

= converges

\frac{\partial}{\partial y} (- 6 x e^{y})

n = 0 \sum \infty (5 n + 1) (- x)^{n}

x \to (1) + lim (x - 1)

ln (x + x^{2} + 1)

f (x) = \frac{1}{1 + e ^{- x}}

What is the sum from n=0 to infinity of e^{(-9n)/2} ?
The sum from n=0 to infinity of e^{(-9n)/2} is converges