Question

The number of rational terms in the binomial expansion of \((4^{1/4}+5^{1/6})^{120}\) is _________.

Answer 1

T_r+1 = ¹²⁰C_r(4^1/4)^120−r⋅(5^1/6)^r

= ¹²⁰C_r⋅2^(60−r/2)⋅5^r/6

For T_r+1 to be rational, r must be divisible by 6.

r = 0,6,12,…,120

Number of rational terms = 21

Answer 2

Answer is: 21

for rational terms r = 6λ 0 ≤ r ≤ 120

so total no of forms are 21.