1. The problem statement, all variables and given/known data(adsbygoogle = window.adsbygoogle || []).push({});

Sorry, I posted this earlier but I had an error in my problem statement; please advise. Thank you.

If a_n diverges to +inf, b_n converge to M>0; prove a_n*b_n diverges to +inf

2. Relevant equations

3. The attempt at a solution

My attempt follows: I seem to have trouble getting things in the right order, so I am trying to work on my technique, with your help. Also, I am afraid I may have omitted reference to some theorem that I am taking for granted, which is another of my bad habits. Please review for me and advise as appropriate. I am determined to conquer this subject! Thanks.

Let M, e > 0, M, e \in R. By definition of a limit of a sequence, we can choose N_b such that |b_n - M|< e, n >= N. Then -e < b_n - M < e, so M - e < b_n < M + e. So b_n > M - e. We can then choose N_a such that a_n >= M/(M-e), n >= N. Let N = max (N_b, N_a). Then a_n*b_n >= M/(M-e), n >= N. Thus, {a_n*b_n} diverges to + infinity.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Sequence: product of sequences diverges

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