Question

In the expansion of $(1+x{)}^{50}$, the sum of the coefficient of odd powers of x is

• A. $2^{49}$
• B. \N
• C. $2^{50}$
• D. $2^{51}$

Answer 1

The correct option is A $2^{49}$

We have, $(1+x{)}^{50}=\sum _{r=0}^{50}{}^{50}{C}_r{x}^r$
Therefore, sum of coefficients of odd power of
$x{=}^{50}{C}_1{+}^{50}{C}_3+......{+}^{50}{C}_{49}$
$=\frac{1}{2}{[}^{50}{C}_0{+}^{50}{C}_1+.....{+}^{50}{C}_{50}]=\frac{1}{2}[2^{50}]=2^{49}.$