What is the value of r? If 2nCr=2nCr+1.

Answer 1

(2n)! / r! (2n-r)! = (2n)! / (r+1)! ( 2n-r-1)!

First you cross multiply

Then (2n)! cancels out

The following equation remains:

(r+1)! ( 2n-r-1)! = r! (2n-r)!

r = 2n-r <--- divides both sides by r! and (2n-r-1 )!

2r = 2n

r = n