Science:Math Exam Resources/Courses/MATH103/April 2012/Question 01 (f)/Solution 1

Recall that

$\displaystyle \ln(1-x)=-x-{\frac {x^{2}}{2}}-{\frac {x^{3}}{3}}-\cdots ,$

therefore

$\displaystyle x\ln(1-x)=-x^{2}-{\frac {x^{3}}{2}}-{\frac {x^{4}}{3}}-\cdots$

The coefficient of x³ term is -1/2 and so the correct answer is D.