Coefficient is $x^{19}$ in $(x - 1) (x - 2) (x - 3) . . . . . . . . . . . . (x - 20)$ is

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Solution

$(x - 1) (x - 2) (x - 3) . . . . . . (x - 20)$ has $20$ roots
i.e, $x = 1, 2, 3......18, 19, 20$
We know sum of roots $= \frac{- c o e f f . o f x^{19}}{c o e f f . x^{20}}$
$= 1 + 2 + 3...... + 20$ $= \frac{- c o e f f o f x^{19}}{1}$
$∴$ coeff of $x^{19} = - 210$

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