Question: How does MAPLE do that?


I asked Maple to evaluate (using "evalf") an infinite sum and it says (very quickly) that the answer is identically 0 (not 10^(-7)).

When I numerically  evaluate a large number of terms of the sum, the answer gets smaller as the number of terms increases, so it seems that Maple is probably correct. The fact that the answer is immediate suggest that Maple is doing some analysis rather than adding a large number of numerical values.

I'd like to know how Maple came to its conclusion because it is a pretty interesting one.

Normally, one can trace Maple's logic by 'debug', 'trace' and 'showstat' commands, but according to the "help", "showstat" will not work with 'evalf' (and it doesn't).

But only with 'evalf' do I get the miraculous zero result.

So, is there any way to trace what Maple did to come to its conclusion in this case?

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