How do you show that (2n)!/[(n!)(2^(n+1))] is not an integer? Any hints or tips are appreciated.
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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.
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
This can be done head-on . . . Show that is not an integer.
We have: . . . . . . . . . . . . . . . . . . .
The numerator is the product of odd integers. . . Hence, it is odd . . . of the form
Therefore: . is not an integer.
Thanks for the help!
Btw, how do you get the numbers to look so neat?
Originally Posted by ezong Thanks for the help!
Btw, how do you get the numbers to look so neat? 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/
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