- #1
MP14
- 5
- 0
Prove by mathematical induction:
(2n)! < (2^(2n))*(n!)^2 , for all n=2,3,4...
I know that to start you must prove that it is true for n=2,
(2*2)! = 24 < 64 = (2^4)(2!)^2
Then you assume that n=k and show tha n=k implies that n=(k+1)
(2k)! < (2^(2k))*(k!)^2
... At this point I am completely lost, I don't know where to go from here to turn it into (k+1)
Any help would be greatly appreciated.
Thanks!
(2n)! < (2^(2n))*(n!)^2 , for all n=2,3,4...
I know that to start you must prove that it is true for n=2,
(2*2)! = 24 < 64 = (2^4)(2!)^2
Then you assume that n=k and show tha n=k implies that n=(k+1)
(2k)! < (2^(2k))*(k!)^2
... At this point I am completely lost, I don't know where to go from here to turn it into (k+1)
Any help would be greatly appreciated.
Thanks!