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With infinite sums, the summand is evaluated. Since Q functions always return True or False, EvenQ[x] evaluates to False since x is not an even integer. You can use Mod instead and everything works fine for your examples. Sum[x/x! Boole[Mod[x,2] == 0], {x, 1, Infinity}] // FullSimplify Sinh[1]


look at: Sum[(x/x!) Boole[EvenQ[x]], {x, 1, Infinity}] // Trace the function Sum (in the case of infinity Sum) try to organize its argument which result in some evaluation. in this case, Boole[EvenQ[x]] evaluated to 0 because EvenQ[x] evaluated to False.

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