What is the sum from n=0 to infinity of (6^n)/(7^n) ?

The sum from n=0 to infinity of (6^n)/(7^n) is converges

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sum from n=0 to infinity of (6^n)/(7^n)

n = 0 \sum \infty \frac{6 ^{n}}{7 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{6 ^{n}}{7 ^{n}}

n \to \infty lim (n (\frac{\frac{6 ^{n}}{7 ^{n}}}{\frac{6 ^{n + 1}}{7 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

x \to 0 + lim (ln (x) sin (x))

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = - 4, y^{^{'}} (0) = 7

\frac{d ^{2}}{d x ^{2}} (\frac{4 x}{x ^{2} + 1})

\int x^{2020} d x

\frac{d}{d x} (ln (1 - \frac{2}{x}))

What is the sum from n=0 to infinity of (6^n)/(7^n) ?
The sum from n=0 to infinity of (6^n)/(7^n) is converges