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Here's the question:

If {sn} is oscillating and not bounded, and {tn} is bounded, then {sn+tn} is oscillating and not bounded.

True or False?

I have tried for a while to find a counterexample, but I can't. I am leaning towards saying that this is true....but then I have to prove it. Am I correct in saying that it's true?

I have also started trying to prove it, but I'm having a hard time. Any clarification or advice will be appreciated.

CC