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Answer to Question #1948 in Real Analysis for alveen

Question #1948
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
Expert's answer
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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Comments

Assignment Expert
16.03.11, 19:09

You are welcome!

alveen
16.03.11, 03:57

thank u sir..the solution will help me solving my problem...

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