If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the greatest binomial coefficient occurs in which one of the following terms?

Step-by-step solution

The sum of binomial coefficients in the expansion of (x + y)^n is 2^n . 2^n = 256 2^n = 2^8 n = 8 In the expansion of (x + y)^8 , the number of terms is n + 1 = 9 . The greatest binomial coefficient occurs at the middle term. Since n = 8 is even, the middle term is the ( n 2 + 1) -th term. Middle term = 8 2 + 1 = 5 The greatest binomial coefficient occurs in the fifth term. Answer: Fifth