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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: solution YOUR ACCURACY IS MUCH BETTER: | Comment 11 of 12 |
(In reply to solution by Dej Mar)

YOUR ACCURACY IS MUCH BETTER:

ACCEPT  n as an average:

{1014049 +1015056)/2=1014552.5
1014552-1014512=40.

40.5/1014512=3.992*10^(-5)  or about 0.004 %


  Posted by Ady TZIDON on 2012-03-17 15:05:20
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