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)
https://cs.stackexchange.com/a/55606/99669
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.