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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: An eleven terms solution | Comment 20 of 31 |
(In reply to An eleven terms solution by e.g.)

e.g.: Excellent job. For those who might be skeptical, I offer the following.

The product of your numbers is P=5832x10^10 the square of which is then P^2=34012224x10^20. Summing P^2 divided by the square of each of your numbers does give exactly P^2/2:

(8503056 + 3779136 + 2125764 + 1360488.96 + 944784 + 236196 + 37791.36 + 13604.8896 + 3401.2224 + 1511.6544 + 377.9136)x10^20 = 17006112x10^20.

 


  Posted by Richard on 2004-09-21 21:40:53
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