What is the sum from n=0 to infinity of (3^n)/(7^n) ?

The sum from n=0 to infinity of (3^n)/(7^n) is converges

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sum from n=0 to infinity of (3^n)/(7^n)

n = 0 \sum \infty \frac{3 ^{n}}{7 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{3 ^{n}}{7 ^{n}}

n \to \infty lim (n (\frac{\frac{3 ^{n}}{7 ^{n}}}{\frac{3 ^{n + 1}}{7 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

n = 0 \sum \infty \frac{2 n - 1}{2 ^{n}}

n = 1 \sum \infty \frac{10}{n ^{2}}

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

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

n = 1 \sum \infty (\frac{2}{n})^{4}

What is the sum from n=0 to infinity of (3^n)/(7^n) ?
The sum from n=0 to infinity of (3^n)/(7^n) is converges