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.

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