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Summing inverses II (Posted on 2012-03-16) Difficulty: 3 of 5
The sum of the reciprocal of the square root of all the positive integers up to n is denoted by F(n), that is:

F(n) = 1+1/√2 + 1/√3 +...+ 1/√n

Determine the maximum value of n such that the integer part of the base ten expansion of F(n) DOES NOT exceed 2012.

*** For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
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re(2): computer solution- my accuracy | Comment 6 of 12 |
(In reply to re: computer solution by K Sengupta)

Guided by your remark I've changed 2012 to 2013 in my initial equation. The new result is n=int(1005.5^2)=1014512.

 Conparing with the number obtained by performing direct evaluation i.e. 1013042 (Charlie) my error is about  .14%


  Posted by Ady TZIDON on 2012-03-16 19:41:15
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