Question

${}^n{C}_0-{\frac{1}{2}}^n{C}_1+{\frac{1}{3}}^n{C}_2-...........+(-1{)}^n\frac{{}^n{C}_n}{n+1}$ =

• A. n
• B. 1/n
• C.
• D.

Answer 1

The correct option is C

Trick : Put n = 1, 2

At n = 1, ${}^1{C}_0$ - $\frac{1}{2}$${}^1{C}_1$ = 1 - $\frac{1}{2}$ = $\frac{1}{2}$

At n =2, ${}^2{C}_0$ - $\frac{1}{2}$${}^2{C}_1$ + $\frac{1}{3}$${}^2{C}_2$ = 1 - 1 + $\frac{1}{3}$ = $\frac{1}{3}$

which is given by option (c).