What is the sum from n=1 to infinity of (n!)/((3n)!) ?

The sum from n=1 to infinity of (n!)/((3n)!) is converges

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sum from n=1 to infinity of (n!)/((3n)!)

n = 1 \sum \infty \frac{n !}{( 3 n ) !}

converges

Solution steps

n = 1 \sum \infty \frac{n !}{( 3 n ) !}

Apply Series Ratio Test:

converges

= converges

i = 0 \sum \infty i

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

n = 0 \sum \infty n - n

lim (k = 0 \sum 7 (- \frac{2}{5})^{k})

n = 2 \sum \infty \frac{3}{5 ^{n}}

What is the sum from n=1 to infinity of (n!)/((3n)!) ?
The sum from n=1 to infinity of (n!)/((3n)!) is converges