If a_n --> 0 and there is a sequence b_n that is bounded, then a_n * b_n --> 0
I am lost on how to prove this.
Since we only know that b_n is bounded, it doesn't necessarily converge or have a limit?
So how do I go about proving that a_n * b_n has a limit?
you should know that we say the limit of a sequence exists and equals iff
For every , there is some such that implies
what can you do with that?
when you get a bit more experienced with that approach, then you can use more sophisticated approaches, like the squeeze theorem, which is what i would use here. what can you say about ?