Middle Term in Binomial Expansion
Consider (x + y)n = nC0xn + nC1xnā1y + nC2 xnā2 y2 + ... + nCnyn
- The middle term depends upon the value of n.
- If n is even, then the total number of term in the expansion is odd. So, there is only one middle term, i.e., term is the middle term.
- If n is odd, then the total number of terms in the expansion is even. So, there are two middle terms, i.e., and are two middle terms.
- Middle term always carries the greatest binomial coefficient. As when n is even middle term Tn/2 + 1 has the greatest binomial coefficient nCn/2. Similarly, when n is odd middle terms T(n+1)/2 and T(n+3)/2 or has the greatest binomial coefficients