What is the sum from n=0 to infinity of (n!)/((2n)!) ?

The sum from n=0 to infinity of (n!)/((2n)!) is converges

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sum from n=0 to infinity of (n!)/((2n)!)

n = 0 \sum \infty \frac{n !}{( 2 n ) !}

converges

Solution steps

n = 0 \sum \infty \frac{n !}{( 2 n ) !}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of (n!)/((2n)!) ?
The sum from n=0 to infinity of (n!)/((2n)!) is converges