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Summing inverses II (Posted on 2012-03-16) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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re: computer solution | Comment 3 of 12 |
(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

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