Asimov> In[1]:= Limit[Abs[Sin[x]]^(1/x), x -> Infinity] Out[1]= 1 But on the RHS of In[1] inside the limit, it takes the value 0 for arbitrarily large x. --Dan Just poaching your irresistable (despite spellcheck resistince) subject line, In[365]:= N[Sum[Sin[n]/Log[n], {n, 2, ∞}]] <brown disclaimers> Out[365]= 0.683914 In[366]:= N[Sum[Sin[n]/Log[n], {n, 2, ∞}], 21] <longer brown disclaimers, but sooner> Out[366]= -2.90772260714548440205*10^28 In[369]:= N[Integrate[Sin[x]/Log[x], {x, 2, ∞}], 26] Out[369]= -0.0964377 In[370]:= N[Integrate[Sin[x]/Log[x], {x, 2, ∞}], 27] <frantic brown diclaimers> Out[370]= -8.24193564681189931453106429*10^34 Boy, them low order digits can sneak up on you. --rwg