Worksheets/Infinite Series Convergence

In this worksheet we study the convergence behavior of the series:

$ \sum_{i=1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6} $

References

Basel problem: https://en.wikipedia.org/wiki/Basel_problem

Proving the series converges (multiple ways): https://www.youtube.com/watch?v=9euTxoCC8Hk

Background on other convergent series: https://plus.maths.org/content/infinite-series-surprises