the first four terms in the expansion of (1-x)^n are 1-6x+ax^2+bx^3.find the n and also the respective value for a and b

Answer 1

(1-x)^n
= 1 + n(-x) + n(n-1)/2! (-x)^2 + n(n-1)(n-2)/3! (-x)^3 + ...

= 1-6x+ax^2+bx^3

so -nx = -6x
n = 6

n(n-1)/2! (-x)^2 = ax^2
6(5)/2=a
a = 15

n(n-1)(n-2)/3! (-x)^3 = bx^3
6(5)(4)/6 = -b
b = -20