I have no idea what I am doing...Please Help!!! . Suppose that {a n } and {b n }

Question

I have no idea what I am doing...Please Help!!! . Suppose that {an} and {bn} are sequencesof positive terms and that Prove that limn--> an =+ if and only if limn--> bn= +. . It says to compare this question to another one. But I don'tunderstand the other one either so it wasn't much help to me. ButI'll put it anyway in case it helps you guys. The other questionwas "Is is possible to have an unbounded sequence {an}so that limn--> [(an) / n] = 0?Explain." I only need the answer to the first problem but if the secondone helps then you are more than welcome to use it. Please Helpme!!!!!!!!

Explanation / Answer

Take the contrapositive. If a_n has a finite limit h1 then, h1 divided by the limit ofb_n, if it is finite, then is positive (because terms werepositive) or 0. If it is 0 it means b_n must be infinite, butbecause of hypothesis L>0, so b_n is finite. The converse, again contrapositive gives, that if b_n has finitelimit then, of course a_n is finite if the quotient is.

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