Theorem
Using Binomial theorem, prove that:


Proof:




\ Hence (ii) is proved.

Note 1:
The L.H.S of (ii) and (iii) will have only finite number of terms, because nCr = 0 in case r>n.
Note 2:
nC0, nC1, ..... nCn are called binomial coefficients. nC0, nC2 nC4, ..... are called even binomial coefficients. nC1, nC3, nC5 .... are called odd binomial coefficients.
Note 3:
In case of no ambiguity, the binomial coefficients nC0, nC1, ..... nCn are written as C0, C1, ..... Cn.
Note 4:
The last term in L.H.S of (ii) and (iii)will depend on the fact as to whether n is even or odd.
Working rules for solving problems:
Rule 1:
If n
N, then

Rule 2:
If n
N, then


Rule 3:
If n
N, then

