What is the sum from n=0 to infinity of (3^n)/(10^n) ?

The sum from n=0 to infinity of (3^n)/(10^n) is converges

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sum from n=0 to infinity of (3^n)/(10^n)

n = 0 \sum \infty \frac{3 ^{n}}{1 0 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{3 ^{n}}{1 0 ^{n}}

n \to \infty lim (n (\frac{\frac{3 ^{n}}{1 0 ^{n}}}{\frac{3 ^{n + 1}}{1 0 ^{n + 1}}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

n = 0 \sum \infty (- 3)^{n}

j = 1 \sum \infty 3^{- 4 j}

n = 1 \sum \infty ln (\frac{10}{n})

n = 0 \sum \infty \frac{1}{π ^{n}}

n = 1 \sum \infty \frac{9}{n} - \frac{9}{n ^{2}}

What is the sum from n=0 to infinity of (3^n)/(10^n) ?
The sum from n=0 to infinity of (3^n)/(10^n) is converges