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.

|an bn| = |an| |bn| < M |an| , n=1,2,....

The infinitesimal& sequence multiplied by some constant is also convergent with limit 0.

## Comments

Assignment Expert16.03.11, 18:09You are welcome!

alveen16.03.11, 02:57thank u sir..the solution will help me solving my problem...

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