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.
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