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

A Fourier transform pair is given by $${\left( {{2 \over 3}} \right)^n}$$ u $$\left[ {n + 3} \right]\,\mathop \Leftrightarrow \limits^{FT} \,{{A{e^{ - j6\pi f}}} \over {1 - \left( {{2 \over 3}} \right){e^{ - j2\pi f}}}}$$ ,
where u(n) donotes the unit step sequence. The values of A is_______________.

Let x(n) = $${\left( {{1 \over 2}} \right)^n}$$ u(n), y(n) = $${x^2}$$, and Y ($$({e^{j\omega }})\,$$ be the Fourier transform of y(n). Then Y ($$({e^{jo}})$$ is