The ABCD parameters of the following 2-port network are

The value of $$\sum\limits_{n = 0}^\infty n {\left( {{1 \over 2}} \right)^n}$$ is ________________.

Let $$\widetilde x\left[ n \right]\, = \,1 + \cos \left[ {{{\pi n} \over 8}} \right]$$ be a periodic signal with period 16. Its DFS coefficients are defined by
$${a_k}$$ = $${1 \over {16}}\sum\limits_{n = 0}^{15} {\widetilde x} \left[ n \right]\exp \left( { - j{\pi \over 8}kn} \right)$$ for all k. The value of the coeffcients $${a_{31}}$$ is _____________________.

A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input x[n ] , the response y[ n] is