This proof is invalid because the series is conditionally convergent, but perhaps it can be extended by introducing an error term of some sort.
Edit: Wait... I'm not confident in this solution all of the sudden..
I'm not quite sure how the last step (technically second to last, where you conclude that the sum but with is replaced with tends to zero) is achieved in your proof? Your answer is correct though. I'll leave it for someone else to do, unless no one else wants to?
I'm not quite sure how the last step (technically second to last, where you conclude that the sum but with is replaced with tends to zero) is achieved in your proof? Your answer is correct though. I'll leave it for someone else to do, unless no one else wants to?