In the expansion of (1-2x)^11 the coefficient of x^3 is k times the coefficient of x^2. Evaluate k.

Question

In the expansion of (1-2x)^11 the coefficient of x^3  is k times  the coefficient of x^2. Evaluate k.

Reiny · Answer

(1-2x)^11 = 1 + 11(-2x) + 55(-2x)^2 + 165(-2x)^3 + ... = 1 - 22x + 220x^2 - 1320x^3 + ... so (220)k = -1320 k = -6