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Limiting Mean (Posted on 2010-03-07) Difficulty: 2 of 5
Evaluate:

Limit H(m)/m
m → ∞

where, H(m) denotes the harmonic mean of the m positive integers m+1, m+2, ....., 2m.

As a bonus, evaluate this limit:

Limit R(m)/m
m → ∞

where, R(m) denotes the root mean square (RMS) of the m positive integers m+1, m+2, ....., 2m.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Similar approach - bonus - Solution? | Comment 2 of 3 |
By a method similar to my previous post, I would suggest the answer to the bonus is sqrt(7/3).  Again a spreadsheet analysis shows that this is the value to seems to be converging for larger "m"
  Posted by Kenny M on 2010-03-07 22:43:33
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