Limit P_n(m)/m
m → ∞

where, P_n(m) denotes the n^thpower mean of the m positive integers m+1, m+2, ....., 2m.

Next, evaluate this limit:

Limit L_n(m)/m
m → ∞

where, L_n(m) denotes the n^th Lehmer mean of the m positive integers m+1, m+2, ....., 2m.

Note: both answers will be formulas in terms of n.