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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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Solution re(2): computer solution | Comment 5 of 12 |
(In reply to re: computer solution by K Sengupta)

Now that it's been pointed out that the floor function is being used, the actual maximum n is now reported as 1,014,512:

 1014512         2012.9998709610511462372139893534503476331543873529710835851278
72041538471431695884054555529916175762818247640111935579433356077474757038366765
43376959673765993615506656884
 1014513         2013.0008637825930489395254365864923254861510870608979421904176
57855182488051462521256587842576557011840593492298355150329749666383799191437091
384938602785675066364028255597


  Posted by Charlie on 2012-03-16 16:57:55
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