Binomial Theorem

Binomial Theorem Binomial Series Introduction When we expand a power of a binomial expression we get a polynomial which can be considered as a series. It is not an arithmetic or geometric one but there is definitely a pattern. eg.

The same pattern occurs in each row. 1. The expansion or series contains (n+1) terms 2. The powers of x (the 1st term ) decrease by 1 in each successive term 3. The powers of y (the second term) increase by 1 in each successive term 4. The sum of the indices add up to n in each term

7. If we detach the coefficients and display them in a triangular array we see more patterns.

This triangle is known as Pascal's triangle and is very useful for finding the coefficient in the binomial expansion.