The coefficient of $x^{49}$ in the product of $(x - 1) (x - 3) . . . . (x - 99)$

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Solution

$\begin{matrix} T h e c o e f f i c i e n t o f x^{49} i n t h e p r o d u c t (x - 1) (x - 2) . . . . (x - 99) H e r e, N u m b e r o f f a c t o r s = 50 ∴ t h e c c o e f f i c i e n t o f x^{49} = (- 1 - 3 - 5..... - 99) = - (1 + 3 + 5 + . . . . + 99) = \frac{- 50}{2} (1 + 99) = \frac{- 50}{2} \times 100 = - 2500 \end{matrix}$

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x^{49}

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