If coefficient of x49 in the product (x - 1) (x - 2) (x-3).......... (x - 50) is

Question

If coefficient of x49 in the product (x - 1) (x - 2) (x-3).......... (x - 50) is (A) -2250 (B) -1275 (C) 1275 (D) 2250

Tardigrade Admin · Accepted Answer

(x - 1) (x - 2) (x - 3 ) .......... (x - 10) = x50 - x49 (1 + 2 + 3 + ......... + 10) + ....... ∴ co.eff of of x49 = - (1 + 2 + ...... + 10) = - (50(50 1)/2) = - 25 × 51 = -1275

Q. If coefficient of $x^{49}$ in the product $(x - 1) (x - 2) (x - 3) .......... (x - 50)$ is

-2250

-1275

1275

2250

$(x - 1) (x - 2) (x - 3) .......... (x - 10)$
$= x^{50} - x^{49} (1 + 2 + 3 + ......... + 10) + .......$
$∴$ co.eff of of $x^{49} = - (1 + 2 + ...... + 10)$
$= - \frac{50 ( 50 1 )}{2}$
$= - 25 \times 51 = - 1275$

Q. If coefficient of x49 in the product (x−1)(x−2)(x−3)..........(x−50) is