In the expansion f (71/3 + 111/9)6561, the number of terms free from radical is ?

General term,

Clearly,  will be free from radical signs, if are integers for

r = 0, 9, 18, 27, ...6561

0, 9, 18, ...6561 is in A.P.

First term, a = 0

Common – difference = 18 – 9 = 9

Last term, t = 6561

l = a + (n – 1)d, where n = number of terms

Hence, number of terms free from radical are 730.

  • 31
What are you looking for?