Infinite Product Examples
The Wallis product is used to calculate the value of and is defined as:
; from n=1 to
To find an approximation of \(\pi\), we can compute the product by taking a finite number of terms. The more terms we use, the closer the approximation will be to the actual value of .
Let's calculate an approximation of using the Wallis product with 10 terms:
Finally, to find an approximation of , we multiply the above result by 2:
=
As we used only 10 terms in the Wallis product, this is a relatively rough approximation. The more terms we include in the product, the more accurate the approximation of will be.