Question

If $S_1$ = ${}^n{C}_0$ + ${}^n{C}_1$ + ${}^n{C}_2$..................${}^n{C}_n$ and $S_2$ = ${}^n{C}_0$ - ${}^n{C}_1$ + ${}^n{C}_2$....................${}^n{C}_n$

Find ${}^n{C}_1$ + ${}^n{C}_3$ + ${}^n{C}_5$..............

• A. $S_1+S_2$
• B. $\frac{S_1-S_2}{2}$
• C. $\frac{S_2-S_1}{2}$
• D. $S_1+S_2$

Answer 1

The correct option is B

$\frac{S_1-S_2}{2}$

$S_1$ - $S_2$ = 2(${}^n{C}_1$ + ${}^n{C}_3$ + ${}^n{C}_5$.....................)

⇒ ${}^n{C}_1$ + ${}^n{C}_3$ + ${}^n{C}_5$................. = $\frac{S_1-S_2}{2}$