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)

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