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error with Sum and Infinity


Hi experts,

i'm very new to Mathematica and this is my first problem. I define a
function that is 0 everywhere:
t[i_] := 0
expect for point i =3 that is:
 t[3] = 1
If now i evaluate the finite sum i obtain 1 as expected
Sum[ t[i], {i, 1, 10}]
Out = 1
but if i try do the same with infinity i obtain
In[808]:= Sum[ t[i], {i, 1, Infinity}]
Out[808]= 0
instead of 1 expected. Any advice?

tb


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