Theorem - Binomial Series

... 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. Pascal's Triangle We want to find a general expansion for the expression To do this, we will look at the first few values of n There are 2 things to

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