- #1

Nana

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## Homework Statement

If a_n+b_n and a_n-b_n converge then a_n and b_n must converge.

This MAY be a counterexample problem.

## Homework Equations

N/A

## The Attempt at a Solution

I have tried the following possibilities out of a_n and b_n and none of these give a counterexample:

Let a_n and b_n= (-1)^n , 1/n , 1/n^2 , (-1)^2n , sqrt(n)

I need to come up with something similar to this that holds true that a_n+b_n converge, a_n-b_n converge, but a_n and b_n alone do not converge.

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