Without direct evaluation, find the minimum integer value of r in this expression :
1+1/√2+1/√3+......+1/√2018 ≤ r*√2018
Note: Adapted from a problem which appeared at Round 1 of Singapore Mathematical Olympiad Open, 2018.
When the result is directly calculated brute force, the result is about 1.9677392, so I suppose this is the minimum value, or the exact value for r (± precision error).
When 10^7 is substituted for 2018, the result is about 1.9995382.
I suspect the limit as n approaches infinity is 2. I suspect the intent was to find the minimum integer value for r: 2.
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Posted by Larry
on 2025-02-20 13:10:38 |
Brute force
