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Wallis product can be stated as the infinite product
The tantalizing statement can be proved by the application of integrals, which is quite unexpected, yet an approach that is quite logical to follow by observing the on one side.
That in fact is the exact method Wallis used to prove it, by integration, by comparing for even and odd values of and using the fact that increasing by 1 results in a change that decreases the change in as gets larger and larger.
This proof does not require integration (see this problem Wallis Product Proof).