How to calculate an infinite sum?

Question

Mathematics

The crux of the matter is that I don't quite understand how exactly to calculate it. How can an infinite sum be calculated in general (more precisely, I understand that it can be calculated using the mathematical apparatus, but how should it look in the code?), any language will do
5 task

Answer 1

1) sum=0; n=0;
2) calculate S(n)
3) if S(n)>ε then 4) otherwise exit
4) sum+=S(n); n++;
5)Go to 2)