If the number of integral terms in the expansion of 3 1 2 + 5 1 8 n is exactly 33 , then the least value of n is

Step-by-step solution

3 1 2 + 5 1 8 n General term T r + 1 = C r n 3 1 2 n - r 5 1 8 r T r + 1 = C r n 3 n - r 2 5 r 8 . n - r 2 ,   r 8 must be integer. n - r 2 ∈ I ⇒ n - r = 0 ,   2 ,   4 ,   6 ,   8 . . . . . . . r 8 ∈ I ⇒ r = 0 ,   8 ,   16 ,   24 ,   32 . . . . For rational term common powers = 0 ,   8 ,   16 ,   24 . . . . . . . Number of integral term = 33 T s = a + s - 1 d   ⇒ T 33 = 0 + 33 - 1 8 = 256 . Value of n = 256 . We can cross