Sigma sums problem

Question

Could you please help me with the below result?

How do we get from here

$(1+2\sum_{j=1}^\infty\rho^j)π_0=1$

To here

$π_0=(1-\rho)/(1+\rho)$

Many thanks

score 2 · Accepted Answer · answered May 22 '14 at 12:18

2

Hint: If $\lvert \rho \rvert < 1$, then you can sum the GP : $\displaystyle \sum_{j=1}^\infty \rho^j = \dfrac{\rho}{1-\rho}$

answered May 22 '14 at 12:18

Macavity

Many thanks for the help! I understand it now. – user152674 May 22 '14 at 12:24
Either you are missing an $-1$ on the right side or the sum has to start with $j=0$ – May 22 '14 at 12:25
Sorry, I misread you right side as $\frac{1}{1-\rho}$. – May 22 '14 at 12:33

1 Answers1