What is the sum from n=0 to infinity of (6^n)/(5^n) ?

The sum from n=0 to infinity of (6^n)/(5^n) is diverges

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sum from n=0 to infinity of (6^n)/(5^n)

n = 0 \sum \infty \frac{6 ^{n}}{5 ^{n}}

diverges

Solution steps

n = 0 \sum \infty \frac{6 ^{n}}{5 ^{n}}

n \to \infty lim (n (\frac{\frac{6 ^{n}}{5 ^{n}}}{\frac{6 ^{n + 1}}{5 ^{n + 1}}} - 1)) = - \infty

L < 1,

by the Raabe's test

= diverges

n = 1 \sum \infty \frac{1}{2 n + 9}

n = 1 \sum \infty n^{9} (1 + n^{10})

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

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

n = 1 \sum \infty (- \frac{5}{6})^{n}

What is the sum from n=0 to infinity of (6^n)/(5^n) ?
The sum from n=0 to infinity of (6^n)/(5^n) is diverges