1. The problem statement, all variables and given/known data My analysis study guide asks me to prove the following: If a_n is a sequence of real numbers whose only subsequential limit in the extended reals is finite, then a_n is bounded. 2. Relevant equations 3. The attempt at a solution Is it right to say that since it has only one subsequential limit, call it L, which is finite in the extended reals (meaning we were considering infinity, so it for sure does not diverge), then since a_n is a subsequence of itself, then it also converges to L? If this were true, I know how to show it is bounded. What makes me think this is wrong is that, below the problem, the study guide asks "additionally, show that a_n is convergent under the above conditions." But I was gonna use its convergence to show its boundedness.. any help appreciated! got a big test coming up next week.