11. Let $\alpha$ be an irrational number, and let the simple continued fraction expansion of $\alpha$ be $\alpha=\left[a_{0} ; a_{1}, a_{2}, \ldots\right]$. Let $p_{k} / q_{k}$ denote, as usual, the $k$ th convergent of this continued fraction. We define the pseudoconvergnts of this continued fraction to be
$$p_{k, t} / q_{k, t}=\left(t p_{k-1}+p_{k-2}\right) /\left(t q_{k-1}+q_{k-2}\right)$$
where $k$ is a positive integer, $k \geqslant 2$, and $t$ is an integer with $00$ such that
$$|\alpha-r / s| \leqslant\left|\alpha-p_{k, t} / q_{k, t}\right|$$
where $k$ is a positive integer and $0q_{k, t}$ or $r / s=p_{k-1} / q_{k-1}$.
d) Find the pseudoconvergents of the simple continued fraction of $\pi$ for $k=2$.
11. d) $\frac{25}{8}, \frac{47}{15}, \frac{69}{22}, \frac{91}{29}, \frac{113}{36}, \frac{135}{43}, \frac{157}{50}, \frac{179}{57}, \frac{201}{64}, \frac{223}{71}, \frac{245}{78}, \frac{267}{85}, \frac{289}{92}, \frac{311}{99}$