Let n ≥ 5 be an integer. If 9 n - 8 n - 1 = 64 α and 6 n - 5 n - 1 = 25 β , then α - β is equal to:

Step-by-step solution

Using the binomial expansion 1 + x n = C 0 n + C 1 n x + C 2 n x 2 . . . . . . . + C n n x n We get, α = 1 + 8 n - 8 n - 1 64 = C 2 n + C 3 n 8 + C 4 n 8 2 + … Similarly β = C 2 n + C 3 n 5 + C 4 n 5 2 + … . So α - β = C 3 n 8 - 5 + C 4 n 8 2 - 5 2 + … + C n n 8 n - 2 - 5 n - 2 So, option (C) is the answer.