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

Engineering

Mathematics

Properties of Binomial Coefficients

Question

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

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

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

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

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

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⁵⁰C₀ + ⁵⁰C₂ · 2² + ⁵⁰C₄ · 2⁴ + …… + ⁵⁰C₅₀ · 2⁵⁰ = $\frac{1}{2}$ (3⁵⁰ + 1)