# Which Method is used during the processing of Sum Function?

I am trying to find out which Method is used while evaluating the following function:

Sum[1/((n^2)), {n, 1, Infinity}]


Any help would be greatly appreciated. A more generic answer would also be helpful but it has to first unambiguously resolve this question. And the extension would be helpful if it clarifies what are the parameters being passed to a method and the syntax etc.

I am a beginner and happy to delete this question if the same is answered elsewhere. But please see below a partial list of what I tried:

I have tried the below options (perhaps with mistakes) and attempted to make sense of the material in the below pages and have been unsuccessful. I have also tried numerous searches on google with different keywords (Such as "Mathematica Sum Function Method" etc ...

How to find out which method Mathematica selected? (Tried changing NDSolve to Sum and other variations);

Also looked at a few other questions that are trying to understand the intermediate steps in Mathematica: Determining the default Method used in optimization and root-finding algorithms What method does NDSolve use for solving PDEs? Determining which rule NIntegrate selects automatically

https://reference.wolfram.com/language/ref/Sum.html

https://reference.wolfram.com/language/tutorial/SomeNotesOnInternalImplementation.html#5107

https://reference.wolfram.com/language/ref/TracePrint.html

• Maybe: AssociationMap[ Sum[1/n^2, {n, 1, Infinity}, Method -> #] &, SumSumMethodDump$availableSumMethods].Only TableLookUp,RationalFunction,HypergeometricTermPFQ,IteratedSummation,Automatic method's works. Aug 30, 2020 at 9:21 • @MariuszIwaniuk AssociationMap fails with the error message, AssociationMap::invrp: The argument SumSumMethodDump$availableSumMethods is not a valid Association or a list. Aug 30, 2020 at 17:54
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