Prove that if the sequence (an) is convergent with the limit 0, and the sequence (bn) is bounded, then the sequence (an bn ) is convergent with limit 0
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Expert's answer
2011-03-15T06:21:21-0400
If {bn} is bounded there exists such M > 0 that |bn| < M at any n. Thus |an bn| = |an| |bn| < M |an| , n=1,2,.... The infinitesimal& sequence multiplied by some constant is also convergent with limit 0.
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