Coupon Accepted Successfully!


Middle Term in Binomial Expansion

Consider (x + y)n = nC0xn + nC1xnā€“1y + nC2 xnā€“2 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., 67155.png 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., 67149.png and 67143.png 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 67137.png has the greatest binomial coefficients 67131.png

Test Your Skills Now!
Take a Quiz now
Reviewer Name