Solution
= Solution
{c}
The equilibrium of the <first-order linear recurrence> is $n/2$. Subtracting it gives
$$
r_{k+1}-n/2=(1-2/n)(r_k-n/2).
$$
Consequently
$$
\boxed{r_k=\frac n2+\frac n2\left(1-\frac2n\right)^k,\qquad k\geq0.}
$$
For $n=2$, interpret the formula at $k=0$ through the initial condition: $r_0=2$, while $r_k=1$ for $k\geq1$. For every $n\geq2$, $r_k\to n/2$.