Prove that for n 2 2 nC2 nC1 n2 nC2 is n choose 2 or n 2

Prove that for n >=2 , 2 nC2 + nC1 = n^2

nC2 is n choose 2 or (n 2)

nC1 is n choose 1 or (n 1)

Proeethatfor? 2.2(2)-G)- Provethat forn > 2.2(?) + n 71 n2

Solution

Sol:

nc2=n(n-1)/2

Given LHS=2 nC2 + nC1

=2[n(n-1)/2]+n

=2[n²-n/2]+n

2 in NR and DR gets cancelled

=n² -n+n

-n and +n gets cancelled

=n²

   ^=RHS