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# summing arctangents Watch

1. I have the following example .

By using arctangent addition, I've gotten to , but the answer is , so how do I eliminate all other solutions?
2. Consider complex numbers say such that , where and consider the argument of .
3. (Original post by B_9710)
Consider complex numbers say such that , where and consider the argument of .
I understand the complex number argument approach, but I'm wonderinh what I'm doing wrong with addition.
4. (Original post by Ayman!)
I have the following example .

By using arctangent addition, I've gotten to , but the answer is , so how do I eliminate all other solutions?
Well, note that for example, are all positive terms, so you know that the sum is bounded below by , furthermore, note that each term is bounded above by (obviously), so the sum is bounded above by and the only integers that satisfies is .
5. (Original post by Zacken)
Well, note that for example, are all positive terms, so you know that the sum is bounded below by , furthermore, note that each term is bounded above by (obviously), so the sum is bounded above by and the only integers that satisfies is .
That second term of your inequality should be n*pi, not just n, surely?
6. (Original post by HapaxOromenon3)
That second term of your inequality should be n*pi, not just n, surely?
Whoop, sorry. Typo there, I meant . Thanks.

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