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.