What is the sum from n=4 to infinity of (5^n)/(14^n) ?

The sum from n=4 to infinity of (5^n)/(14^n) is converges

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sum from n=4 to infinity of (5^n)/(14^n)

n = 4 \sum \infty \frac{5 ^{n}}{1 4 ^{n}}

converges

Solution steps

n = 4 \sum \infty \frac{5 ^{n}}{1 4 ^{n}}

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

L > 1,

by the Raabe's test

= converges

n = 2 \sum \infty \frac{5}{n ^{3}}

n = 0 \sum \infty \frac{( 0.8 ) ^{n}}{7}

n = 1 \sum \infty (\frac{n}{2 n})^{n}

n = 1 \sum \infty \frac{2 n}{5 n - 1}

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

What is the sum from n=4 to infinity of (5^n)/(14^n) ?
The sum from n=4 to infinity of (5^n)/(14^n) is converges