The term independent of x in the expansion of x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 1 0 is

Step-by-step solution

We know, x 2 / 3 - x 1 / 3 + 1 x 1 / 3 + 1 = x + 1 ⇒ x + 1 x 2 / 3 - x 1 / 3 + 1 = x 1 / 3 + 1 Also, x - 1 x - x = x - 1 x + 1 x x - 1 = x + 1 x = 1 + x - 1 / 2 Hence, the given binomial becomes x 1 / 3 - x - 1 / 2 10 . General term = 10 C r - 1 r x 10 - r 3 x - r 2 Hence, for term independent of x . We get 10 - r 3 = r 2 20 - 2 r = 3 r r = 4 ∴ Term Independent of x = 10 C 4 = 210