If C 0 ,   C 1 ,   C 2 ,   … … C n denotes the binomial coefficients in the expansion of ( 1 + x ) n , then the value of C 0 + C 1 2 + C 2 3 + . . . + C n n + 1 is equal to

Step-by-step solution

We know that , 1 + x n = C 0 + C 1 x + C 2 x 2 + … + C n x n On integrating both sides, from 0 to 1, we get 1 + x n + 1 n + 1 0 1 = C 0 x + C 1 x 2 2 + C 2 x 3 3 + … + C n x n + 1 n + 1 0 1 ⟹ 2 n + 1 - 1 n + 1 = C 0 + C 1 2 + C 2 3 + . . . + C n n + 1