What is the sum from n=0 to infinity of (5^n)/(3^n) ?

The sum from n=0 to infinity of (5^n)/(3^n) is diverges

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sum from n=0 to infinity of (5^n)/(3^n)

n = 0 \sum \infty \frac{5 ^{n}}{3 ^{n}}

diverges

Solution steps

n = 0 \sum \infty \frac{5 ^{n}}{3 ^{n}}

n \to \infty lim (n (\frac{\frac{5 ^{n}}{3 ^{n}}}{\frac{5 ^{n + 1}}{3 ^{n + 1}}} - 1)) = - \infty

L < 1,

by the Raabe's test

= diverges

What is the sum from n=0 to infinity of (5^n)/(3^n) ?
The sum from n=0 to infinity of (5^n)/(3^n) is diverges