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P/Q (Posted on 2012-10-12) Difficulty: 4 of 5
Evaluate P/Q, given:

P= 1-2-2+4-2-5-2+7 -2-8-2+10-2 -11-2+13-2-14-2+...

Q= 1+2-2-4-2-5-2+7 -2+8-2-10-2 -11-2+13-2+14-2+...


No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: computer solution | Comment 4 of 5 |
(In reply to computer solution by Charlie)

Charlie, I agree.

When the sum of the expression I supplied earlier is correctly evaluated from 0 to infinity, the result is indeed 2/3:

(sum_(n=0 to infinity) (1/(1+6n)^2+1/(4+6n)^2-1/(6n+2)^2-1/(6n+5)^2))/ (sum_(n=0 to infinity) (1/(6n+1)^2+1/(6n+2)^2-1/(6n+4)^2-1/(6n+5)^2)) =2/3,

since (4 (psi(1, 1/3)-psi(1, 2/3)))/(psi(1, 1/6)+psi(1, 1/3)-psi(1, 2/3)-psi(1, 5/6)) is 0.6 recurring. (psi is the polygamma function)

 

 

Edited on October 13, 2012, 10:35 am
  Posted by broll on 2012-10-13 09:11:52

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