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Binomial Theorem and its proof by Inductive method

Updated on September 17, 2012

Introduction

Let us start with simple equation:

we all know that

(a+b)0 = 1

and if we want to go to the next levels then

(a+b) 1 = a+b

(a+b)2 = (a+b)*(a+b) = a2+b2+2ab

(a+b)3 = (a+b)*(a+b)*(a+b) = a3+b3+3a2b+3ab2

now, what if we want to expand (a+b) with higher powers?

It would become a very tedious work and for these kind of binomial expansions with higher powers, we have a theorem called Binomial Theorem which can expand any power for (a+b).

Binomial Theorem is a fundamental theorem in Algebra that is used to expand expressions of the form (a+b)n.

Definition and Inductive Proof :

Binomial Theorem is defines as follows:

For any integer positive integer n

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