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Math Help - Cal II infinite series homework questions...

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Cal1981 View Post
    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
    .
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