I believe that infinite sums are usually defined in terms of limits, which is why I said that both examples were limits.<p>&gt; By definition, limits approach their target values, they never equal them -- otherwise we would accept division by zero and similar things.<p>I think I would say that a convergent sequence (most of the time that one cares) does not ever reach the target value (though, eventually constant sequences do, but those aren&#x27;t interesting), but that the limit of the convergent sequence is equal to &#x2F; is the target value. As opposed to saying that &quot;the limit approaches&quot;. The limit isn&#x27;t the thing that changes with another thing, but the limit of some changing?