Proving a theorem about limits

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The discussion revolves around proving that if the limit of the sequence \( s_n \) approaches 0 as \( n \) approaches infinity, and \( (t_n) \) is a bounded sequence, then the limit of the product \( s_n t_n \) also approaches 0. The user initially struggled with the proof but received a hint to consider the bounded nature of \( t_n \) and its relationship with \( s_n \). Ultimately, the user concluded that demonstrating \( M s_n \) tends to zero, where \( M \) is the bound of the sequence \( t_n \), is key to solving the problem.

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a) Suppose that the limit as n goes to infinity sn=0. If (tn) is a bounded sequence, prove that lim(sntn)=0.
So I need to show that abs(sntn)<epsilon, and I know that abs(sn)<epsilon. I mean, I know abs(sntn)=abs(sn)abs(tn that didn't help.
I don't know how to go about this. I've tried the triangle inequality variations but that didn't seem to get me anywhere either. I feel like I'm going in circles.
can I get a hint?

thanks!
 
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say M is a bound of the sequnce t_n, can you show M.s_n tends to zero?
 
thanks, I finally figured it out!
mjjoga
 

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