TOPICS

Introduction

Binomial Theorem

The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is (a + b)^{n} = ^{n}C_{0}a^{n} + ^{n}C_{1}a^{n-1}b + ^{n}C_{2}a^{n-2}b^{2} + ...+ ^{n}C_{n-1}a.b^{n-1} + ^{n}C_{n}b^{n}.

The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle.

The general term of an expansion (a + b)^{n} is T_{r+1} = ^{n}C_{r}a^{n-r}b^{r}. In the expansion (a + b)^{n}, if n is even, then the middle term is the (n/2 + 1)th
term. If n is odd, then the middle terms are (n + 1)/2 th and [(n + 1)/2 + 1] th terms.

CLASSES