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Timeless Theorems of Mathematics/Binomial Theorem
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The Binomial Theorem is a fundamental theorem in algebra that provides a formula to expand powers of binomials. It allows us to easily expand expressions, , where and are real numbers or variables, and .
Proof
Proposition: For any real numbers and
Where
Proof (Mathematical Induction):
For
For
For
For
Let's assume for some Now we just have to show that the equation holds true for
Or,
∴