What is the sum from n=0 to infinity of (4^n)/(5^n) ?

The sum from n=0 to infinity of (4^n)/(5^n) is converges

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sum from n=0 to infinity of (4^n)/(5^n)

n = 0 \sum \infty \frac{4 ^{n}}{5 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{4 ^{n}}{5 ^{n}}

n \to \infty lim (n (\frac{\frac{4 ^{n}}{5 ^{n}}}{\frac{4 ^{n + 1}}{5 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

f (x) = (3 x + 70)^{50}

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

y^{^{''}} + 6.2832 y = 0

n = 0 \sum \infty (\frac{4}{5})^{n}

\int 18 t e^{t} d t

What is the sum from n=0 to infinity of (4^n)/(5^n) ?
The sum from n=0 to infinity of (4^n)/(5^n) is converges