Q17 of 118 Page 18

For all positive integers n, show that

Given that we need to prove .

Consider L.H.S:

We know that ⁿC_r + ⁿC_{r + 1} = ^{n + 1}C_{r + 1}

⇒ ²ⁿC_n + ²ⁿC_{n – 1} = ^{2n + 1}C_n

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

= R.H.S

∴ L.H.S = R.H.S, thus proved.

If α = ^mC₂, then find the value of ^αC₂.

Prove that the product of 2n consecutive negative integers is divisible by (2n)!

Prove that : ⁴ⁿC_2n : ²ⁿC_n = [1 . 3 . 5 …. (4n – 1)] : [1.3.5….. (2n – 1)]².

Evaluate