How Euler discovered some values of the Riemann Zeta function

Using generating functions, we find the values of some infinite sums. In the process, we come across the Riemann Zeta function, the Dirichlet Eta function and the Dirichlet Beta function. To describe the values, we introduce the Bernoulli numbers and the Euler numbers. Finally we look at the values of these functions at negative integers. Math animations are made using Manim