The coefficient of x - 5 in the binomial expansion of x + 1 x 2 3 - x 1 3 + 1 - x - 1 x - x 1 2 10 where x ≠ 0,1 is

Step-by-step solution

x 1 3 + 1   x 2 3 - x 1 3 + 1 x 2 3 - x 1 3 + 1 - x - 1   x + 1 x   x - 1 10 = x 1 3 + 1 - 1 - 1 x 1 2 10 = x 1 3 - x - 1 2 10 t r + 1 = 10 C r x 1 3 10 - r x − 1 2 r ( − 1 ) r t r + 1 = 10 C r x 10 3 - 5 r 6 - 1 r ∵   10 3 - 5 r 6 = - 5 5 r 6 = 50 6     ⇒ r = 10 Hence, 10 C 10 - 1 10 = 1