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

Find the missing sequence in the letter series below:
A, CD, GHI, ? , UVWXY

If x>y>1, which of the following must be true? $$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;\;\;\;\;\mathrm{ii}.\;\;\mathrm e^\mathrm x>\mathrm e^\mathrm y\\\mathrm{iii}.\;\mathrm y^\mathrm x>\mathrm x^\mathrm y\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{iv}.\;\cos\left(\mathrm x\right)>\cos\left(\mathrm y\right)\end{array}$$$