- #1

fk378

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## Homework Statement

If the sum(a_n) and the sum(b_n) are both divergent, is the sum(a_n + b_n) necessarily divergent?

## The Attempt at a Solution

At first I thought it must be divergent, but then I asked, what if a_n is 1/n and b_n is -1/n... then their sum would be 0.

Does this logic make sense? And if so, would it imply that sum(a_n + b_n)=0, and is therefore convergent?