Number of integral terms in the expansion of 7 1 2 + 11 1 6 824 is equal to ______.

Step-by-step solution

We know that, General term in expansion of ( 7 ) 1 / 2 + ( 11 ) 1 / 6 824 is given by, t r + 1 = C r 824 · 7 824 - r 2 · 11 r 6 For integral term, r must be multiple of 6 and should be less than 824 So, the series will be r = 0 , 6 , 12 , . . . . . 822 Now, finding number of terms we get, 822 = 0 + n - 1 6 ⇒ 137 = n - 1 ⇒ n = 138 Hence, total integral terms will be 138