# Thread: Cal II infinite series homework questions...

1. ## Cal II infinite series homework questions...

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

Problem 2.
http://i13.photobucket.com/albums/a2...g?t=1257213228

2. Originally Posted by Cal1981
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

$f(x)=\frac{4x}{(1-4x)^2}=\frac{1}{4x}\,\frac{1}{\left(1-\frac{1}{4x}\right)^2}$

But $\frac{1}{1-x}=\sum\limits_{n=0}^\infty x^n\,\Longrightarrow \frac{1}{(1-x)^2}=\sum\limits_{n=1}^\infty nx^{n-1}\,,\;|x|<1$

Thus: $\frac{1}{4x}\,\frac{1}{\left(1-\frac{1}{4x}\right)^2}=\frac{1}{4x}\sum\limits_{n= 1}^\infty n(4x)^{-n+1}=\sum\limits_{n=1}^\infty n(4x)^{-n}$

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
.