In polynomial (x - 1)(x - 2)(x - 3).............(x - 100), coefficient of {x^{99}} is

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7.Binomial Theorem

hard

In the polynomial $(x - 1)(x - 2)(x - 3).............(x - 100),$ the coefficient of ${x^{99}}$ is

A

$5050$

B

$-5050$

C

$100$

D

$99$

Solution

(b) $(x – 1)(x – 2)(x – 3)….(x – 100)$

Number of terms $= 100;$

Coefficient of $x^{99} = (x – 1)(x – 2)(x – 3)…(x – 100)$

= $( – 1 – 2 – 3 – …… – 100)$ = $ – (1 + 2 + ….. + 100)$

= $ – \frac{{100 \times 101}}{2} = -5050.$

Standard 11

Mathematics

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