fails on oscillatory series! Slightly nicer than the one we were doing: (c182) product(1-(-1)^n/sqrt(n),n,1,inf) inf /===\ n | | (- 1) (d182) | | (1 - -------) | | sqrt(n) n = 1 Sum((-)^n/sqrt(n)) converges, but grouping terms pairwise: (c183) resimplify(linchange(%,2*n-1)) inf /===\ | | 1 1 (d183) | | (1 - ---------------) (------------- + 1) | | sqrt(2) sqrt(n) sqrt(2 n - 1) n = 1 (c184) taylor(first(%),n,inf,1) 1 (d184)/T/ 1 - --- + . . . 2 n I.e., the product diverges to zero. (<=> the sum of the logs diverges to -oo.) I don't remember being warned about this. With pairwise grouping, Mathematica knows In[111]:= Product[(1 - (1/(Sqrt[2]*Sqrt[n])))*((1/(Sqrt[2*n - 1])) + 1), List[n, 1, Infinity]] Out[111]= 0 It doesn't even say "Divergent". Why should it? Infinite Product and Sum notation mean "Take the limit". By this reasoning, Sum[1/n, {n, Infinity}] should just shut up and return Infinity. --Bill