What is the sum from n=6 to infinity of (5^n)/(10^n) ?

The sum from n=6 to infinity of (5^n)/(10^n) is converges

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sum from n=6 to infinity of (5^n)/(10^n)

n = 6 \sum \infty \frac{5 ^{n}}{1 0 ^{n}}

converges

Solution steps

n = 6 \sum \infty \frac{5 ^{n}}{1 0 ^{n}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{1 0 ^{n}}}{\frac{5 ^{n + 1}}{1 0 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

\int \frac{tan ^{3} ( \frac{2}{z} )}{z ^{2}}

\frac{d y}{d x} + x y = y^{4}

\int \frac{x + 9}{x ^{2} + 9} d x

\frac{\partial}{\partial x} ((x^{2} - 3 y) (x - 2))

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

What is the sum from n=6 to infinity of (5^n)/(10^n) ?
The sum from n=6 to infinity of (5^n)/(10^n) is converges