Question

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

• A. 2⁴⁹
• B.
• C.

Answer 1

The correct option is A 2⁴⁹

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