What is the sum from n=0 to infinity of (5^n)/(8^n) ?

The sum from n=0 to infinity of (5^n)/(8^n) is converges

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sum from n=0 to infinity of (5^n)/(8^n)

n = 0 \sum \infty \frac{5 ^{n}}{8 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{5 ^{n}}{8 ^{n}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{8 ^{n}}}{\frac{5 ^{n + 1}}{8 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

\frac{2 x ^{3}}{5}

\int_{1}^{2} \frac{3}{x ^{4}} d x

\frac{d r}{d θ} = \frac{r ^{2} + 4 r θ}{2 θ ^{2}}

f (x) = x^{4} + 3 x - 2, (1, 2)

x \to 0 - lim (2^{\frac{1}{x}})

What is the sum from n=0 to infinity of (5^n)/(8^n) ?
The sum from n=0 to infinity of (5^n)/(8^n) is converges