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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

d er i v a t i v e x^{4} + \frac{4}{3} x^{3} - 4 x^{2} - \frac{4}{3}

\int \frac{y + 1}{y ^{2} + 1} d y

t an g e n t f (x) = 5 x^{3} - 5 x, (- 1, 0)

\int x (4 x + 5)^{3} d x

im pl i c i t \frac{d y}{d x}, x y = 28

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