Quick binomial expansion using GC

Binomial expansion can be done quickly using the GC.

Consider binomial expansion of , where a is a real number, and q is a fraction or negative integer.

The recurrence formula for the coef works out to be

Example 1

Expand   in ascending powers up to and including the term in 

Using TI 84 Plus (OS 2.55)

Therefore, the expansion is

The recurrence formula can also be used to expand in descending powers of x.

Example 2

Expand  in descending powers of x up to the 7th term.

Using TI 84 Plus (OS 2.55)

Therefore, the expansion is