math
posted by mel gibbs on .
Express (5x+2)/(2x1)(x+1) into partial fractions and hence expand the expression as a series in ascending power of x giving the first 4 terms

(5x+2)/(2x1)(x+1)
= 3/(2x1) + 1/(x+1)
Now, think of geometric series where the infinite sum is
S = a/(1r)
3/(2x1) = 3/(12x) = 3(1+(2x)+(2x)^2 + (2x)^3)
= 3(1+2x+4x^2+8x^3)
= 3  6x  12x^2  24x^3
Similarly for 1/(x+1) so we end up with
2  7x  11x^2  25x^3  ...