I have two multiple choice homework problems that I can't get. I've linked the scanned problems below. These are due tomorrow morning and I am stumped. Can someone please help? Thanks!

Problem 1.

http://i13.photobucket.com/albums/a2...g?t=1257212983 $\displaystyle f(x)=\frac{4x}{(1-4x)^2}=\frac{1}{4x}\,\frac{1}{\left(1-\frac{1}{4x}\right)^2}$ But $\displaystyle \frac{1}{1-x}=\sum\limits_{n=0}^\infty x^n\,\Longrightarrow \frac{1}{(1-x)^2}=\sum\limits_{n=1}^\infty nx^{n-1}\,,\;|x|<1$ Thus: $\displaystyle \frac{1}{4x}\,\frac{1}{\left(1-\frac{1}{4x}\right)^2}=\frac{1}{4x}\sum\limits_{n= 1}^\infty n(4x)^{-n+1}=\sum\limits_{n=1}^\infty n(4x)^{-n}$ The correct option seems to be (B) but I can't distinguish the minus in the power of 4x... Tonio Ps. One problem each time
Problem 2.

http://i13.
photobucket.com/albums/a284/chris_lisauckis/Misc/img154.jpg?t=1257213228