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 computer solution by Charlie)

Charlie, I am a big fan (and, will always remain so) of your accurate solutions to the problems.

However, this problem asks for the maximum value of n such that the integer part of the base ten expansion of F(n) DOES NOT exceed 2012, that is: Floor(F(n)) < 2013, while your solution deals with maximum n such that Floor(F(n)) < 2012.

Accordingly, you may wish to revise your calculations in light of the foregoing.

Edited on March 16, 2012, 2:20 pm

Posted by K Sengupta on 2012-03-16 14:18:30