if p is a prime no satisfying n<p<2n show that
2n
C is divsible be p...............
n
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3 Answers
39i say u better search the forum once...
i remember having seen this one before here
62this one is pretty simple btw..
Hint and Solution
p divides (2n!)
but p does not divide n! (since it does not divide any prime number less than n)
1i solved it but was not getting the time to post it
it can2n c n can be reduced to the form
2n.2n-1.2n-2.2n-3.2n-4....n-2.n-1/n!
=2(n)2n-1.2(n-1).2n-3.n-2.n-1/n!
therfore n! is cancelled out
since p is aprime number it cant be a multiple of 2 and according to the equation we get p will be one f the n+1,n+3,n+5,2n-1 so it is divisible