\[

B_{1} = A \quad & i \quad p_{1} = Tr[B_{1}] \\
B_{2} = A(B_{1} - p_{1}I) \quad & i \quad p_{2} = \frac{1}{2}Tr[B_{2}] \\
\quad \vdots \\
B_{k} = A(B_{k-1} - p_{k-1}I)  \quad & i \quad p_{k} = \frac{1}{k}Tr[B_{k}] \\
\quad \vdots \\
B_{n} = A(B_{n-1} - p_{n-1}I)  \quad & i \quad p_{n} = \frac{1}{n}Tr[B_{n}] \\

\]