The coefficient of $x^{49}$ in the product $(x - 1) (x - 2) (x - 3) . . . . (x - 50)$ is

- 2250

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- 1275

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1275

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2250

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- 49

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Solution

The correct option is A $- 1275$
Coefficient of $x^{49}$ in product of $(x - 1) (x - 2) (x - 3) (x - 4) . . . . . . . . (x - 50)$
We know that,
$(x - 1) (x - 2) (x - 3) (x - 4) . . . . . . . . (x - n) = x^{n} - (1 + 2 + 3 + . . . . + n) x^{n - 1} + . . . . . . .$
Coefficient of $x^{49} = - (1 + 2 + 3 + . . . + 50)$
$= - \frac{50 \times 51}{2}$
$= - 1275$
Hence, B is the correct option.

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Similar questions

The coefficient of x⁴⁹ in the product

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