What is the sum from n=3 to infinity of (5^n)/(14^n) ?

The sum from n=3 to infinity of (5^n)/(14^n) is converges

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sum from n=3 to infinity of (5^n)/(14^n)

n = 3 \sum \infty \frac{5 ^{n}}{1 4 ^{n}}

converges

Solution steps

n = 3 \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

\int x \cdot e^{4 x} d x

x = 4 y^{3}, x = 22 y^{2}

\frac{d}{d x} (4 x - x^{3})

\int \frac{x ^{2} + 2 x}{x ^{3} + 3 x ^{2} - 5} d x

\frac{\partial}{\partial x} (8 x y^{2} - 8 x^{3} y)

What is the sum from n=3 to infinity of (5^n)/(14^n) ?
The sum from n=3 to infinity of (5^n)/(14^n) is converges