# How to calculate the sum of a general series

In class we learned how to test the convergence of series and how to calculate the sums of arithmetic and geometric series (if they exist) but are there methods to actually calculate the values non-arithmetic, non-geometric series? Can the value of any series be calculated or only those of a certain type? And can it still be done if they're infinite? So my question is: are there any general methods for calculating the values of certain non-arithmetic/geometric series (references would be appreciated as well) [because it seemed like a lot of effort for Euler just to calculate the sum from n=1 to infinity of $\frac1{n^2}$]. Thanks in advance!

No, there is no general way to calculate a "general series" because there are just so many series, they can be very involved. There are even very simple finite sum like $\sum_{i=1}^n 1/i$ that have no simple closed form.