Sunday, 5 February 2012

The Binomial Expansion part 2, (1+x)^n Expansion

This is part 2 of the Binomial Expansion topic. In this I will show to expand the expression (1+x)^n. Here n is any real number, and the modulus of (x) must be less than 1.

 You will learn Modulus function later on in c3, it is basically the positive form for any real number. The though the proper definition would be the distance away from 0 on the real number line, remember distance meaning length, (length can't be negative), so modulus denoted |A| = Modulus of A. Don't worry about this for now, it's just knowing how to use the formula :

The formula is / Binomial Series :

Let's assses line 1, which states :

(1+x)^alpha = The sum of all terms starting from k=0 till infinity, of the binomial coefficient (alpha k)* x^k.

Where the binomial coefficient is :

The difference between the Binomial Theorem and Binomial Series is that the Binomial Theorem, is just a rule for expanding an expression (x + y)^n... the Binomial Series is the sum of the terms of the sequence, this can be finite or infinite. I will post some examples below soon !