What is the sum from n=3 to infinity of (7^n)/(14^n) ?

The sum from n=3 to infinity of (7^n)/(14^n) is converges

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sum from n=3 to infinity of (7^n)/(14^n)

n = 3 \sum \infty \frac{7 ^{n}}{1 4 ^{n}}

converges

Solution steps

n = 3 \sum \infty \frac{7 ^{n}}{1 4 ^{n}}

n \to \infty lim (n (\frac{\frac{7 ^{n}}{1 4 ^{n}}}{\frac{7 ^{n + 1}}{1 4 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

x \to \infty lim (2 + \frac{5}{x})

\int \frac{e ^{- x^{2}}}{x} d x

\frac{d}{d x} (ln (\frac{1 - x}{1 + x}))

x \to 0 lim ((1 + 5 x)^{\frac{6}{x}})

\int 5 cos (x^{2}) d x

What is the sum from n=3 to infinity of (7^n)/(14^n) ?
The sum from n=3 to infinity of (7^n)/(14^n) is converges