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.