I a reading an article in neural coding. It cintains a limit which I cannot understand. (It remindes the benomial sum but it didn't work for me) I am talking about $(22) \Rightarrow (23)$ in the picture below.
Any help? Thanks!
EDIT
The problem here is to show that, as $N \log{f} \to 0$,
$$\left (1-f^{-N} \right )^{p-1} \sum_{S=0}^{p-2} \binom{p-1}{S} \left (f^{N}-1 \right ) \log_2{\left (\frac{p}{S+1} \right )} \sim (p-1)\log_2{\left (\frac{p}{p-1} \right )} N \log{f}$$
Actually, this is a fairly straightforward procedure. Recognize that $f^N = e^{N \log{f}}$. Then as $N \log{f} \to 0$,
$$\left ( 1-f^{-N} \right)^{p-1} \sim (N \log{f})^{p-1} $$ $$\left ( 1-f^{-N} \right)^{-S} \sim (N \log{f})^{-S} $$
Also note that, in the sum, the quantity $(N \log{f})^{-S}$ increases greatly for increasing $S$. Thus, you need only consider the $S=p-2$ term in the sum. Plug the numbers in and you get your Eq. (23).