I don't quite undersand your question.
If you look at 1/1 this gives 1. Next, 1/(1+2) is 1/3 which is roughly 0.33. Then, 1/(1+2+3) is 1/6 which is rougly 0.17 ( i think) If this keeps going as n tends to infinity, the value is going to tend to zero, rather than to 1.