What is the sum from n=0 to infinity of (2^n)/(5^n) ?

The sum from n=0 to infinity of (2^n)/(5^n) is 5/3

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sum from n=0 to infinity of (2^n)/(5^n)

n = 0 \sum \infty \frac{2 ^{n}}{5 ^{n}}

\frac{5}{3}

Solution steps

n = 0 \sum \infty \frac{2 ^{n}}{5 ^{n}}

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= n = 0 \sum \infty (\frac{2}{5})^{n}

Apply Series Geometric Test:

\frac{5}{3}

= \frac{5}{3}

x \to \infty - lim (\frac{1}{x})

x y^{^{'}} = x e^{- 2 x} - (2 x + 1) y

x \to 8 - lim (4 x)

\frac{d}{d x} (c_{2} - 3 c_{1} - 3 c_{2} x)

\int \frac{8}{1 + x ^{2}} d x

What is the sum from n=0 to infinity of (2^n)/(5^n) ?
The sum from n=0 to infinity of (2^n)/(5^n) is 5/3