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(2): computer solution- my accuracy by Ady TZIDON)

1014512 is indeed the exact result based on use of 2013 instead of 2012, but that doesn't equal int(1005.5^2), which is 1011030.

Posted by Charlie on 2012-03-17 00:34:05