Whoa... let me stop you RIGHT here. No one is saying that we sum up an infinite number of terms. What we mean by the limit in that situation above is "what's the least upper bound of the nondecreasing sequence of summations?" Or a bit more loose... what's the smallest number that the sequence gets close to? Draqon... what's the highest level of mathematics you have taken? You're arguing from a layman's point of view it seems. That's fine until you start making incorrect assumptions about notation and definition.