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Get one half by squaring (Posted on 2004-09-20) Difficulty: 4 of 5
Can you solve the following equation?

= 1/x + 1/y +...+ 1/z

All variables must be different, positive integers, and there must be a finite number of terms.

See The Solution Submitted by Federico Kereki    
Rating: 4.2500 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution | Comment 9 of 31 |
(In reply to re: Solution by Richard)

Oops - I didn't realize that Richard had put the exact value of pi^2/6 in his previous post - I only saw the approximation 1.6449 at first glance.  This post adds no new content.  =) 

More specifically, if you've had some differential equations before, you can show that the sum 1/1+1/4+1/9+... + 1/n^2+ ... is equal to PI^2/6.

I like this problem a lot.  Hit a lot of dead ends trying to solve it - always a sign of a great problem.  Still working at it.  Kudos to Frederico. 

Edited on September 20, 2004, 11:05 pm
  Posted by David Shin on 2004-09-20 22:51:37

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