Chapter 3, Problem 3.20TE

(a)

To determine

To calculate:To prove that ${\alpha }_{n+1}={\alpha }_n(p+p\text{'}-1)+1-p\text{'}n\ge 1$ and also prove

  ${\alpha }_n=\frac{1-p\text{'}}{2-p-p\text{'}}+\left(\alpha -\frac{1-p\text{'}}{2-p-p\text{'}}\right)\times {(p+p\text{'}-1)}^{n-1}$ .