Expand 8 / (2 - x)^3 in ascending powers of x up to and including the term in x^2, stating the range of x for which the expansion is valid.
Find the coefficient of x^n in the expansion.
Hi,
Expansion and validity range are basic skills; do look up details in your school's notes.
Coefficient of x^n may be obtained by:
1. looking at the pattern presented by the expansion;
2. considering the general term; and
3. knowing results such as
(a) general term of x^n for the expansion of 1/(1 - x) = x^n,
(b) general term of x^n for the expansion of 1/(1 - x)^2 = (n + 1) x^n,
(c) general term of x^n for the expansion of 1/(1 - x)^3 = (1/2)(n + 1)(n + 2) x^n.
Thanks.
Cheers,
Wen Shih