Hi,

Do you think the following limits are correct?

$\displaystyle\lim_{d\to\infty}\frac{\sum\limits_{k=1}^{d} {\phi(N) \choose k} {d-1 \choose k-1}}{\phi(N)^d}=0$

$\displaystyle\lim_{N\to\infty}\frac{\sum\limits_{k=1}^{d} {\phi(N) \choose k} {d-1 \choose k-1}}{\phi(N)^d}=c$

I plotted the equations and guessed the results according to the graphs but I could not prove them mathematically by myself. Any hints would be appreciated. Graphs are as follows:

http://deniz.cs.utsa.edu/plots/d_vs_Eq.jpeg

http://deniz.cs.utsa.edu/plots/N_vs_Eq.jpeg

Thanks,