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\item  The asymptopic behavior of $h_{m}$ relative to $h_{m'}$ depends on the relationship between m and m' (whether one is larger than the other, or is equal).  $N = \fraction{1-m^{h+1}}{1-m}$ \frac{1-m^{h+1}}{1-m}$  via geometric sum $N(1-m) = 1-m^{h+1}$