Infinite limit of inverse tangent series

Click For Summary

Homework Help Overview

The discussion revolves around evaluating the infinite limit of a sequence related to the inverse tangent function. Participants are exploring the mathematical properties and relationships involving tangent and arctangent functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin the problem and seeks hints. Some participants provide a hint involving the tangent subtraction formula, while others explore specific values for A and B in the context of the tangent function.

Discussion Status

The conversation includes attempts to clarify the relationships between tangent and arctangent functions. Some participants have suggested specific forms for A and B, indicating a productive exploration of the problem. However, there is no explicit consensus on the approach yet.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The original poster's request for hints suggests a need for guidance without direct solutions.

flyerpower
Messages
46
Reaction score
0

Homework Statement


Take the infinite limit of that sequence.
ScreenShot036.jpg
(click to expand)


Homework Equations





The Attempt at a Solution


I have no idea where to start from, hints and ideas would be greatly appreciated.

Thanks.
 
Physics news on Phys.org
hi flyerpower! :smile:

hint: (tanA - tanB)/(1 + tanAtanB) :wink:
 
tiny-tim said:
hi flyerpower! :smile:

hint: (tanA - tanB)/(1 + tanAtanB) :wink:


Ok, so tan(A-B)=(tanA-tanB)/(1+tanAtanB)

and A-B=arctan[(tanA-tanB)/(1+tanAtanB)

Now i think i should find some A and B so as :

tanA-tanB=x
and
tanA*tanB=k(k+1)*x^2

buuut i cannot still figure out what A and B should be
 
How about tan(A) =(k+1)x & tan(B) =kx ?
 
LOL, it was so obvious, thank you:)

It gives me pi/2 - arctg(x) which is arctg(1/x)

Thank you both!
 

Similar threads

Prove that the linear space is infinite dimensional
  • · Replies 18 ·
Replies
18
Views
2K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Is this infinite series convergent or divergent?
  • · Replies 6 ·
Replies
6
Views
2K
How Do You Find the Limit of the Series S_n = \dfrac {3}{8}⋅\dfrac {4^n}{3^n}?
  • · Replies 2 ·
Replies
2
Views
1K
Why the series is divergent based on the Preliminary test
  • · Replies 2 ·
Replies
2
Views
1K
Find the slope of the tangent line to the function's inverse
  • · Replies 13 ·
Replies
13
Views
5K
Showing that partial sums diverge to infinity
  • · Replies 7 ·
Replies
7
Views
2K
Every convergent sequence has a monotoic subsequence
  • · Replies 4 ·
Replies
4
Views
2K
Question about Frechet compactness
  • · Replies 5 ·
Replies
5
Views
1K
Double Integration Homework: Changing Limits
  • · Replies 2 ·
Replies
2
Views
1K