Storage cost of a matrix of size n x n

c[n_]:=n(n+1)/2

For a separable L.S. problem (∑_(i=1)^p)(Subscript[c, i])(Subscript[f, i])(x)~y, the numerator is the storage cost for handling parameters x and c together whereas the denominator is the cost of applying the separable L.S. techniques as described in 
Separable nonlinear least squares
H.B.Nielsen
Technical report IMM-REP-2000-01
http:http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/646/ps/imm646.ps

r[n_,p_]:=c[n+p]/(c[n]p(p+1)/2)

We compute the ratio and plot it

LogLinearPlot[{r[n,2],r[n,3]},{n,1,10^3},PlotRange->{Automatic,{0,1}},GridLines->{None,{1/3,1/6}},PlotStyle->{Thick}]

Asymptotic limits for large n: typical in practice

rl[p_]:=Limit[r[n,p],n->+Infinity]
rl[p]
rl[{1,2,3,4}]