Binomial Theorem

A binomial expression has two terms that are connected by the operators ‘+’ or ‘–’. Binomial theorem helps to expand any power of a given binomial expression. According to binomial theorem expansion of any binomial (a + b)n ,is given by: (a + b)n = nC0 an b0 + nC1 an–1 b1 + nC2 an–2 b2 + … + nCn a0bn The total number of terms in the expansion of (a + b)n, for any positive integral n is (n + 1), i.e., one more than the index. Power of the first quantity ‘a’ go on decreasing by 1, whereas the power of the second quantity ‘b’ increases by 1, in the successive terms. In each term of the expansion of (a + b)n, for any positive integral n, the sum of the indices of a and b is same and equal to n. In the expansion of (a + b)n, coefficients nc0, nc1, nc2, and so on upto ncn are called the binomial coefficients. The general term in the expansion of (a + b)n is given by (r + 1)th term, i.e., Tr+1 = nCr an–r br where 0 ≤ r ≤ n. In case of an even index, number of middle terms in the expansion of (a + b)n is one and is given by [(n/2) + 1]th term. In case of an odd index, number of middle terms in the expansion of (a + b)n are two and are given by [(n+1) / 2]th and [(n+1/2) + 1]th term. Keywords: Pascal’s triangle

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