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The sum of coefficients of integral powers of x in the binomial expansion of (1 − 2√x)⁵⁰ is:

1. 1/2 (3⁵⁰ + 1)
2. 1/2 (3⁵⁰)
3. 1/2 (3⁵⁰ − 1)
4. 1/2 (2⁵⁰ + 1)

Correct answer: 1/2 (3⁵⁰ + 1)

Solution

The sum of the coefficients of the integral powers of x in the binomial expansion can be found by evaluating the expression at x=1. Substituting x=1 into (1 - 2√x)⁵⁰ gives (1 - 2)⁵⁰ = (-1)⁵⁰ = 1. The sum of coefficients is then half of this value, leading to the correct answer of 1/2 (3⁵⁰ + 1).

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