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

Evaluate

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

Find the limit

n \to + \infty lim \frac{\frac{( 2 ( n + 1 ) ) !}{2 ^{n + 1}}}{\frac{( 2 n ) !}{2 ^{n}}}

Simplify

n \to + \infty lim (∣ (n + 1) (2 n + 1) ∣)

Remove the absolute value bars

n \to + \infty lim ((n + 1) (2 n + 1))

Rewrite the expression

n \to + \infty lim (n + 1) \times n \to + \infty lim (2 n + 1)

Calculate

More Steps

(+ \infty) \times n \to + \infty lim (2 n + 1)

Calculate

More Steps

(+ \infty) (+ \infty)

Calculate

+ \infty

Solution

Diverges