The Coefficient with binomial expansion can be arranged in the following triangle pattern named after Blaise Pascal.
If are the terms in the expansion of then the term is called the General term.
It can be verified that term form the beginning and the term form the end which is equal to the term from the beginning
Since , the coefficients of the equidistant terms from the beginning and end are equal.
In the binomial expansion of there are terms. Thus, there is only one middle term is even and there are two middle term if is odd.
(i) Let be even say Then the middle term is equal to
(ii) Let be odd say , then