9709/MayJune/2006/3/Q9

(i) Express 10/(2-x)(1+x^2) in partial fractions. [5]

(ii) Hence, given that |x| < 1, obtain the expansion of 10/(2-x)(1+x^2) in ascending powers of x, up to and including the term in x^3, simplifying the coefficients. [5]

Solution:

Reference: PYQ - May/June 2006 Paper 3 Q9