How do you simplify (2k)!/(2k+2)! to 1/(2(k+1)(2k+1)) ?

Question

6960 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-06T01:11:02

The expression we want to simplify is

$E = ((2k)!)/((2k+2)!)$ .

Since $(2k+2)! = (2k+2)(2k+1)(2k)!$ , then:

$E = ((2k)!)/((2k+2)(2k+1)(2k)!)$ .

Then:

$E = cancel((2k)!)/((2k+2)(2k+1)cancel(2k)!)$ .

This gives

$E = 1/((2k+2)(2k+1))$ .

We can rewrite $(2k+2) = 2(k+1)$ ; then:

$E = 1/(2(k+1)(2k+1))$ .

Hope it helped!