Regularize Divergent Sums and Products
Many divergent sums and products can be given a finite value through regularization. Convergent sums and products produce the ordinary value under regularization.
 In:= ```problems = {HoldForm[ Sum[(-1)^k, {k, 0, Infinity}, Regularization -> "Abel"]], HoldForm[Sum[k*k!, {k, 0, Infinity}, Regularization -> "Borel"]], HoldForm[ Sum[Sin[k], {k, 0, Infinity}, Regularization -> "Cesaro"]], HoldForm[Sum[k, {k, 1, Infinity}, Regularization -> "Dirichlet"]], HoldForm[ Sum[(-1)^k*(k + 1), {k, 0, Infinity}, Regularization -> "Euler"]], HoldForm[ Product[k^2, {k, 1, Infinity}, Regularization -> "Dirichlet"]]};```
 In:= ```FormulaGallery[forms_List] := Module[{vals = ParallelMap[ReleaseHold, forms]}, Text@TraditionalForm@ Grid[Table[{forms[[i]], "==", vals[[i]]}, {i, Length[forms]}], Dividers -> {{True, False, False, True}, All}, Alignment -> {{Right, Center, Left}, Baseline}, Background -> LightYellow, Spacings -> {Automatic, 2}]]```
 In:= `FormulaGallery[problems]`
 Out=  