What is the sum from n=0 to infinity of 5^{-n} ?

The sum from n=0 to infinity of 5^{-n} is 5/4

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sum from n=0 to infinity of 5^{-n}

n = 0 \sum \infty 5^{- n}

\frac{5}{4}

Solution steps

n = 0 \sum \infty 5^{- n}

Simplify

5^{- n} : \frac{1}{5 ^{n}}

= n = 0 \sum \infty \frac{1}{5 ^{n}}

Apply Series Geometric Test:

\frac{5}{4}

= \frac{5}{4}

\frac{d}{d x} (ln (1 + 8 x))

x \to 1 + lim (\frac{1}{x ^{2} + 1})

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

\int (1 - y^{2}) d y

y^{^{''}} + 7 y^{^{'}} + 10 y = - 18 t e^{2 t}

What is the sum from n=0 to infinity of 5^{-n} ?
The sum from n=0 to infinity of 5^{-n} is 5/4