Below is a proof of the relations of binomial coefficients.Sum of product of binomial coefficient (special case)
Other proofs will thoroughly added.This is just a try and will be  updated time to time to make it effective.
.. Sum of product of binomial coefficient (general appraoach)

Introduction to Fourier series Download Now.

A short introduction to Fourier sereis. And analytical derivation of the Fourier coefficients.

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