let {an} and {bn} be Cauchy sequences.  Using teh definition of CAuchy
sequences show that the sum {an + bn} is a CAuchy sequence and the
product is {an*bn} is a Cauchy sequence

Hello fmunshi:

Thanks for the interesting question. 

A good definition of Cauchy sequences can be found at: 

Cauchy sequence
URL: http://www.wikipedia.org/wiki/Cauchy_sequence

I found an excellent proof of both of your questions online. Rather
than reproduce them here, I will point you to the existing solutions.

Sequences and Limits
URL: http://www.math.colostate.edu/~estep/education/517/notesonreals.pdf
Note: Go to page 29 of this 46-page document, Section 11.2, Theorem
11.2 - "A Cauchy sequence of rational numbers is bounded."  There both
{an + bn} and {an*bn} are shown to be Cauchy sequences.

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If that fails as well, please let me know (using the Clarification
Request feature), and I will try to "type" it our for you here.

Thanks. 

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