The following comment on an other question says that if we have an infinite language L that satisfies the pumping lemma for regular languages then we have a word with n≤|w|≤2n which is in L. (n is the constant in the pumping lemma)
Why is this the case? The lower limit can be explained by the constant of the regular pumping lemma, because in infinite languages there exists a word in L which is longer than n.
But how comes there is an upper limit? The pumping lemma does not say anthing about a upper limit for the words we choose.