What is the sum from n=0 to infinity of (7^n)/(11^n) ?

The sum from n=0 to infinity of (7^n)/(11^n) is converges

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sum from n=0 to infinity of (7^n)/(11^n)

n = 0 \sum \infty \frac{7 ^{n}}{1 1 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{7 ^{n}}{1 1 ^{n}}

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

L > 1,

by the Raabe's test

= converges

\int_{0}^{1} \frac{1}{x ^{3}} d x

e^{2} + 2^{x}

x \to 0 + lim (x^{15 x})

n = 5 \sum \infty (\frac{4}{5})^{- n}

9 t

What is the sum from n=0 to infinity of (7^n)/(11^n) ?
The sum from n=0 to infinity of (7^n)/(11^n) is converges