3.1.11

b)

$π_{0} \cdot λ = π_{1} \cdot μ \Rightarrow π_{1} = \frac{π_{0} \cdot λ}{μ} = 2 \cdot \frac{1}{2} \cdot π_{0} \frac{λ}{μ} = 2 π_{0} \cdot \frac{λ}{2 μ} = 2 π_{0} ρ$ $pi_0 * lambda = pi_1 * mu => pi_1=(pi_0*lambda)/mu=2 * 1/2 * pi_0lambda/mu = 2pi_0 * lambda/(2mu)=2pi_0rho$

$π_{1} \cdot λ = π_{2} \cdot 2 μ \Rightarrow π_{2} = 2 π_{0} ρ^{2}$ $pi_1 * lambda = pi_2 * 2mu => pi_2 = 2pi_0rho^2$

$π_{2} \cdot λ = π_{3} \cdot 2 μ \Rightarrow π_{3} = 2 π_{0} ρ^{3}$ $pi_2 * lambda = pi_3 * 2mu => pi_3 = 2pi_0rho^3$

$\Rightarrow π_{i} = 2 π_{0} ρ^{i}$ $=> pi_i = 2 pi_0rho^i$

c)

$1 = π_{0} + π_{1} + π_{2} + ...$ $1 = pi_0 + pi_1 + pi_2 + ...$

$1 = π_{0} + π_{1} 2 ρ + π_{2} 2 ρ^{2} + π_{3} 2 ρ^{3} + ...$ $1=pi_0+pi_1 2rho+pi_2 2rho^2+pi_3 2rho^3+...$

$1 = π_{0} (1 + 2 ρ + 2 ρ^{2} + 2 ρ^{3} + ...)$ $1=pi_0 (1 + 2rho+2rho^2+2rho^3+...)$

$1 = π_{0} (1 + 2 (ρ + 2 ρ^{2} + 2 ρ^{3} + ...)$ $1=pi_0 (1 + 2 (rho+2rho^2+2rho^3+...)$