How do you show that (2n)!/[(n!)(2^(n+1))] is not an integer? Any hints or tips are appreciated.

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- September 22nd 2009, 04:38 PMezongbinomial theorem help
How do you show that (2n)!/[(n!)(2^(n+1))] is not an integer? Any hints or tips are appreciated.

- September 22nd 2009, 04:57 PMTaluivren
Hi!

by induction prove that for some odd :

is clear, .

Supposing for some odd you get

since product of two odd numbers is odd, the inductive step is completed. - September 24th 2009, 09:08 AMRenji Rodrigo
Other solution

we can use the identity

*dividing by*2 in both sides we have that is not an integer , because the first term is a product of odd numbers - September 24th 2009, 02:00 PMSoroban
Hello, ezong!

This can be done head-on . . .

Quote:

Show that is not an integer.

We have: .

. . . . . .

. . . . . .

. . . . . .

Then: .

The numerator is the product of odd integers.

. . Hence, it is odd . . . of the form

Therefore: . is not an integer.

- October 8th 2009, 02:30 PMezong
Thanks for the help!

Btw, how do you get the numbers to look so neat? - October 9th 2009, 04:25 AMTaluivren
Hello ezong, you can learn some basic LaTex typing here: http://www.mathhelpforum.com/math-he...-tutorial.html

and consult in LaTex Help subforum__http://www.mathhelpforum.com/math-help/latex-help/__