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.

integral of x^(-1/2) is 2*sqrt(x)

evaluating from 0 to n we get :

2*sqrt(n)<2012

n<1006^2=1012036

n=1012035

QUICK , BUT DEFINITELY NOT PRECISE

Posted by Ady TZIDON on 2012-03-16 14:37:00