What is the sum from n=0 to infinity of (5^n)/(6^n) ?

The sum from n=0 to infinity of (5^n)/(6^n) is converges

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sum from n=0 to infinity of (5^n)/(6^n)

n = 0 \sum \infty \frac{5 ^{n}}{6 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{5 ^{n}}{6 ^{n}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{6 ^{n}}}{\frac{5 ^{n + 1}}{6 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

x^{2} y^{^{'}} + 3 x y = 1

x^{6} - 4 e^{x}

\int \frac{4}{x} + 4 x d x

\int x \cdot x^{2} d x

e^{x} y y^{^{'}} = e^{- y} + e^{- 2 x - y}

What is the sum from n=0 to infinity of (5^n)/(6^n) ?
The sum from n=0 to infinity of (5^n)/(6^n) is converges