First slide

Series of natural numbers

Question

Coefficient of $x^{99}$ in the expansion of
$(x - 1) (x - 3) (x - 5) \dots (x - 199)$ is

Moderate

A

$- 100$
B

$- 1000$
C

$- 10000$
D

$- 100000$

Solution

Coefficient of $x^{99}$
$= - (1 + 3 + 5 + \dots 199) = - 100^{2} = - 10000$

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