Question

The coefficient of x⁹⁹ in (x –1) (x–2) (x–3) …… (x – 100) is

• A. –5050
• B. 5050
• C. 5000
• D. –5000

Answer 1

Answer: (A)

–5050

Answer 2

Polynomial = x¹⁰⁰ + x⁹⁹ (–1 –2 –3 .… –100) + …

\ coefficient of x⁹⁹ = – (1 + 2 + 3 + …… 100)

= $\frac { - 100 } { 2 } ( 1 + 100 ) = - 5050$