Question

Coefficient of x^1001 in (1-x)^901(1+x+x^2)^900is:

Answer 1

Answer:

(1-x)^901 (1+x+x^2)^900

this above eqn can be written as

(1-x)^900(1+x+x^2)^900(1-x)

this above eqn can be written as

((1-x)(1+x+x^2))^900(1-x)

this above eqn can be written as

(1-x^3)^900(1-x)

since 1001 on factorisation can be written as 7*13*11

and 7 , 13 , 11 are not divisible by 3 so in (1-x^3)^900 coefficient of x^1001 is 0

0(1-x) = 0