Home » Ask & Discuss » Mathematics. » Trignometry « Back to Discussion

Trignometry

Forum Expert

Joined:	28 Feb 2007
Post:	2173

22 Dec 2008 06:59:34 IST

0 People liked this

566

Trig summation

None

Evaluate

Share this article on:

Comments (1)

abhishek sinha

Forum Expert

Joined: 18 Dec 2007

Posts: 913

22 Dec 2008 22:31:37 IST

Like 0 people liked this

Very simple ...

see 2r / (2r^4 +1)

= 4r/ ( 4r^4 +2 )

=4r / {( (2r^2)^2 +1 ) +1}

= 4r/ { 1 + (1+2r^2)^2 -(2r)^2 }

= {( 1+ 2r +2r^2) - ( 1- 2r +2r^2)}/ { 1 + ( 2r^2 +2r + 1)(2r^2 -2r +1)}

so the given qty becomes

arctan ( 2r^2 + 2r +1) -arctan{ 2(r-1)^2 + 2(r-1) +1}

for which upon summing , successive terms cancels leaving the reqd sum to be

arctan ( 2n^2 + 2n +1) - pi/4

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

Free Sign Up!

Preparing for IIT-JEE ?

Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor

@ INR 1,995/-

For Quick Info

Find Posts by Topics

Physics.

Topics

9128

19728

3590

2097

7393

2755

2568

Mathematics.

Chemistry.

Biology

Institutes

Parents

Board

Fun Zone