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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} - \frac{4}{3}

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

f (x) = 5 x^{3} - 5 x, (- 1, 0)

g (x) = \frac{1 + 2 x}{3 - 4 x}

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

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