I need help factorising..
Nk+1 = Nk + rNk(1-Nk/k)
= (1+r -Nk/k)Nk
Apparently that equals..
= (1+r)[1-Nk/(1+r)k]Nk
But i dont see how...
$\displaystyle N_k + r N_k \left(1 - \frac{N_k}{k} \right)$
$\displaystyle = N_k \left[ 1 + r \left(1 - \frac{N_k}{k} \right) \right]$
$\displaystyle = N_k \left[ 1 + r - \frac{r N_k}{k} \right]$
$\displaystyle = N_k \left[ (1 + r) - \frac{r N_k}{k} \right]$
$\displaystyle = N_k (1 + r) \left[1 - \frac{{\color{red}r} N_k}{k (1 + r)} \right]$