Quick binomial expansion using GC

Binomial expansion can be done quickly using the GC.

Consider binomial expansion of Tex2Img_1396931745, where a is a real number, and q is a fraction or negative integer.

The recurrence formula for the coef works out to be

Tex2Img_1396931939

Example 1

Expand Tex2Img_1396932117  in ascending powers up to and including the term in Tex2Img_1396932205

Using TI 84 Plus (OS 2.55)

bin

Therefore, the expansion is

Tex2Img_1396933315

 

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

Example 2

Expand Tex2Img_1397528779 in descending powers of x up to the 7th term.

Using TI 84 Plus (OS 2.55)

1

Therefore, the expansion is

Tex2Img_1397529466

 

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