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.

(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