Question

$\frac{{}^n{c}_0}{n}$ + $\frac{{}^n{c}_1}{n+1}$ + $\frac{{}^n{c}_2}{n+2}$+_ _ _ _ _ _ + $\frac{{}^n{c}_n}{2n}$ =

• A.
• B.
• C.
• D.

Answer 1

Answer: (B), (C)

The correct options are
B

C

Given sum =${}^n{c}_0{\int }_0^1{x}^{n-1}dx{+}^n{c}_1{\int }_0^1{x}^{n}dx+......................{+}^n{c}_n{\int }_0^1{x}^{2n-1}dx$

=${\int }_0^1{[}^n{c}_0.x^{n-1}{+}^n{c}_1.x^n......................{+}^n{c}_n{x}^{2n-1}]dx$

= ${\int }_0^1{x}^{n-1}(1+x{)}^{n}dx$ = ${\int }_1^2(x-1{)}^{n-1}.x^{n}dx$