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  • The coefficient of  in the expansion of <img alt="(x-1)\left(x-\frac{1}{2}\right)\left(x-\frac{1}{2^

The coefficient of x^{49} in the expansion of (x-1)\left(x-\frac{1}{2}\right)\left(x-\frac{1}{2^2}\right) \ldots\left(x-\frac{1}{2^{49}}\right) is equals to

Option: 1

-2\left(1-\frac{1}{2^{50}}\right)


Option: 2

+ve coefficient of x


Option: 3

-ve coefficient of x


Option: 4

-2\left(1-\frac{1}{2^{49}}\right)


Answers (1)

best_answer

coeff... of x^{49} in the series is

-\left[1+\frac{1}{2}+\frac{1}{2^2}+\ldots \ldots+\frac{1}{2^{49}}\right]=-\left[\frac{1-\frac{1}{2^{50}}}{1-\frac{1}{2}}\right]=-2 \cdot\left[1-\frac{1}{2^{50}}\right]

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