You are Here: Home >< Maths

# summing arctangents

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
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.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. Oops, you need to agree to our Ts&Cs to register

Updated: July 12, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.