What is the sum from n=0 to infinity of (5^n)/(7^n) ?

The sum from n=0 to infinity of (5^n)/(7^n) is converges

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sum from n=0 to infinity of (5^n)/(7^n)

n = 0 \sum \infty \frac{5 ^{n}}{7 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{5 ^{n}}{7 ^{n}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{7 ^{n}}}{\frac{5 ^{n + 1}}{7 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

n = 0 \sum \infty n (0. 8^{n})

n = 3 \sum \infty \frac{2}{n ln ^{2} ( n )}

n = 0 \sum \infty - \frac{4}{e ^{n}}

n = 0 \sum \infty \frac{1}{e ^{4 n}}

n = 1 \sum \infty \frac{n + 3}{2 n + 1}

What is the sum from n=0 to infinity of (5^n)/(7^n) ?
The sum from n=0 to infinity of (5^n)/(7^n) is converges