# Test Review 1 - lim sups and lim infs

by cmurphy
Tags: infs, review, sups, test
 P: 30 Hello, I am taking Adv. Calc, and we have a test next week. I am going to post a few questions that I have from the review where I got stuck. If you have any help, please steer me in the right direction! Question 1: Suppose sn <= 0 <= tn for n in N. Prove (lim inf sn)(lim sup tn) <= lim inf (sntn), provided none of these products is of the form 0 * infinity. Here is what I have so far: Since sn <= 0, we must have lim inf sn <= 0. Also, since tn >= 0, we must have lim sup tn >= 0. Thus (lim inf sn)(lim sup tn) <= 0. We also know that (sntn) <= 0. This means that lim inf (sntn) <= 0. I am having difficulties at this point, because the two things that I want to compare are both <= 0, so I don't have a way of comparing them. I'm not sure where to go with this. Any suggestions? Colleen

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