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Binomial Theorem and its proof by Inductive method
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