The Gregory-Leibniz Series

The series which we can use to find the value of π to any degree of accuracy.

Let’s dive in this fascinating series.

We will start by stating that

Note that this result was obtained using the Binomial Theorem.

Integrating,

Or,

Evaluating these integrals,

Substituting x=1,

Hence,

Multiplying by 4,

Now, you may realise that this series will not give a very exact value of π with the first few terms, for example the sum to the first 5 terms is approximately 2.895.

But the sums to the first 101 terms gives us a very close approximation of 3.142.

I hope you enjoyed that!

Thank you for reading, as always.

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