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Infinite series can't really be calculated to completion using a computer,The sum of an infinite divergent series cannot be calculated with or without a computer.
The sum of an infinite convergent series can be calculated with:
1/(a-r)
Sequence > Limits and convergence:
https://en.wikipedia.org/wiki/Sequence#Limits_and_convergenc...Limit of a sequence:
https://en.wikipedia.org/wiki/Limit_of_a_sequence
SymPy docs > Limits of Sequences: https://docs.sympy.org/latest/modules/series/limitseq.html
> Provides methods to compute limit of terms having sequences at infinity.
Madhava-Leibniz formula for π: https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80