Question

how do you simplify (2k!)/((2(k+1))!)

Answer 1

\[note: (ab)! \neq (a!)(b!)\]

Answer 2

\[\frac{2k!}{(2(k+1))!}=\frac{2*k*(k-1)*(k-2)\cdots 2*1}{(2k+2)!}\]

and \((2k+2)!=(2k+2)(2k+1)(2k)(2k-1)\cdots 2*1\)

Answer 3

I don't know if you can simplify this more though. It doesn't seem like it.

Answer 4

I don't think it can be simplified any further

Answer 5

unless you meant (2k)!

Answer 6

@buggiethebug It's so easy!
2(k+1) can be wriiten as (2k+2) and it's factorial will be (2k+2)*(2k+1)*(2k)!.U can cancel 2k! both in numerator and denominator.So u r left with 1/(2k+2)(2k+1)

Answer 7

@quantun that would be true if it's (2k)!. But 2k! isn't the same as (2k)!

Answer 8

@sourwing She mentioned (2k)! , right?
Just see her comment

Answer 9

Where is her comment o.O?

Answer 10

actually my bad its 2k!/(2(k+1))! :/

Answer 11

@buggiethebug still the same u wrote above

Answer 12

do you mean maybe \(2(k+1)!\) maybe then in the denominator? because your expression can be simplified then

Answer 13

no I meant (2(k+1))!

Answer 14

samething