Question

The sum of coefficients of integral powers of $x$ in the binomial expansion $(1-2\sqrt x)^{50}$ is

• A. $\frac{1}{2}(3^{50})$
• B. $\frac{1}{2}(3^{50}+1)$
• C. $\frac{1}{2}(3^{50}-1)$
• D. $\frac{1}{2}(2^{50}+1)$

Answer 1

Answer: (B)

$\frac{1}{2}(3^{50}+1)$

Answer 2

for sum of integral power of $x$ put $x=1$ in $\frac{(1-2 \sqrt{x})^{50}+(1+2 \sqrt{x})^{50}}{2}$ $\Rightarrow \frac{3^{50}+1}{2}$.