What is the sum from n=1 to infinity of ((2n)!)/(n!) ?

The sum from n=1 to infinity of ((2n)!)/(n!) is diverges

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sum from n=1 to infinity of ((2n)!)/(n!)

n = 1 \sum \infty \frac{( 2 n ) !}{n !}

diverges

Solution steps

n = 1 \sum \infty \frac{( 2 n ) !}{n !}

Apply Series Ratio Test:

diverges

= diverges

n = 5 \sum \infty \frac{1}{n !}

n = 0 \sum \infty \frac{3}{3 - 6 n}

k = 1 \sum \infty \frac{1 0 ^{k}}{k !}

n = 1 \sum \infty (n - 1)^{2}

k = 1 \sum \infty \frac{2}{k} - \frac{2}{k + 1}

What is the sum from n=1 to infinity of ((2n)!)/(n!) ?
The sum from n=1 to infinity of ((2n)!)/(n!) is diverges