The number of terms in the expansion of 5 1 6 + 7 1 9 1824 which are integers is

Step-by-step solution

T K + 1 = 1824 C K 5 1824 - K 6 7 K 9 Where, K = 0 , 1 , 2 . . . . . , 1824 Now, 1824 - K 6 will be an integer if K = 0 , 6 , 12 , 18 , . . . . , 1824 Also, K 9 will be an integer if K = 0 , 9 , 18 , . . . . . , 1818 . ⇒ Both are integers if K= 0 , 18 , 36 , . . . . . , 1818 If the number of terms = n , ⇒ 1818 = 0 + n – 1 18 ⇒ n = 102