binomial theorem

LastRide7 SG

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.

wee_ws SG

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,

Thanks.

Cheers,
Wen Shih