The sum of coefficients of integral powers of x in the binomial expansion of 1 - 2 x 50 is

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Question: Answered & Verified by Expert

The sum of coefficients of integral powers of

x

in the binomial expansion of

{(1 - 2 \sqrt{x})}^{50}

is

MathematicsBinomial TheoremJEE MainJEE Main 2015 (04 Apr)

Options:

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

Solution:

2457 Upvotes Verified Answer

The correct answer is:

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

Integral Power Term is same as odd term in exapansion

Odd Term

= \frac{{(1 - 2 \sqrt{x})}^{50} + {(1 + 2 \sqrt{x})}^{50}}{2}

Sum of coefficients

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

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