For all positive integers n, show that
Given that we need to prove .
Consider L.H.S:
We know that nCr + nCr + 1 = n + 1Cr + 1
⇒ 2nCn + 2nCn – 1 = 2n + 1Cn
We know that
And also n! = n(n – 1)(n – 2)…………2.1
⇒
= R.H.S
∴ L.H.S = R.H.S, thus proved.