Results 1 to 11 of 11

Math Help - Help me! This power series is driving me crazy!

  1. #1
    Newbie
    Joined
    Mar 2008
    From
    Chandler, Arizona
    Posts
    16

    Help me! This power series is driving me crazy!

    The function is represented as a power series

    Find the first few coefficients in the power series.
    C0-C5
    and radius of convergence

    I've obtained C0 and the radius of convergence but every other answer I put in keeps coming back as incorrect.
    I'm going by 1/(1-x) = 1 + x + x^2 + ...
    So for C0 I get 1x3=3
    This is where it goes downhill... For C1 I get 3[-100x^2]^1 so C1=-300?? and I sort of repeat this method except each time the final exponent gets larger.
    I found the radius of convergence by doing |100x^2| < 1 so x < 1/10
    Please help with the rest! I've been doing this problem FOREVER and I don't understand why I at very least haven't guessed the answers!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by sgares View Post
    The function is represented as a power series

    Find the first few coefficients in the power series.
    C0-C5
    and radius of convergence

    I've obtained C0 and the radius of convergence but every other answer I put in keeps coming back as incorrect.
    I'm going by 1/(1-x) = 1 + x + x^2 + ...
    So for C0 I get 1x3=3
    This is where it goes downhill... For C1 I get 3[-100x^2]^1 so C1=-300?? and I sort of repeat this method except each time the final exponent gets larger.
    I found the radius of convergence by doing |100x^2| < 1 so x < 1/10
    Please help with the rest! I've been doing this problem FOREVER and I don't understand why I at very least haven't guessed the answers!
    \frac{3}{1+100x^2}=3\cdot\frac{1}{1+(10x)^2}=3\cdo  t\sum_{n=0}^{\infty}(-1)^n(10x)^{2n}

    use the Root test
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    From
    Chandler, Arizona
    Posts
    16


    use the Root test
    What do you mean by "use the root test"? How will that help me find the coefficients?
    Also, using your formula and simply plugging in n=1, n=2, n=3, and n=4 I received the coefficients 3, -300, 30000, -30000000, 300000000... these are the same answers I was receiving prior to this, and they were all wrong besides the first one.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by sgares View Post
    What do you mean by "use the root test"? How will that help me find the coefficients?
    Also, using your formula and simply plugging in n=1, n=2, n=3, and n=4 I received the coefficients 3, -300, 30000, -30000000, 300000000... these are the same answers I was receiving prior to this, and they were all wrong besides the first one.
    You asked for the radius of convergence, and that is the right power series.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2008
    From
    Chandler, Arizona
    Posts
    16
    I believe you that it is the correct power series, but why am I getting incorrect answers for the coefficients then? Is it something wrong with my calculations or with my webwork? Also, I stated that I already calculated the radius of convergence, and it was 1/10.

    As I just stated, I received the coefficients 3, -300, 30000, -30000000, 300000000, and the final four of these are incorrect. Why though? :\
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by sgares View Post
    I believe you that it is the correct power series, but why am I getting incorrect answers for the coefficients then? Is it something wrong with my calculations or with my webwork? Also, I stated that I already calculated the radius of convergence, and it was 1/10.

    As I just stated, I received the coefficients 3, -300, 30000, -30000000, 300000000, and the final four of these are incorrect. Why though? :\
    That should be right...why do you say it is wrong?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Mar 2008
    From
    Chandler, Arizona
    Posts
    16
    I don't know man... I'm so flustered at this point from this problem! Grrr!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,079
    Thanks
    375
    Awards
    1
    It is probably because you have found the first five nonzero coefficients. I suspect the answer is
    3, 0, -300, 0, 30000

    -Dan
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Mar 2008
    From
    Chandler, Arizona
    Posts
    16
    Woah, that was correct topsquark... thank you so much for that lol. I still have no idea why that is correct though, so if anyone could explain this to me that would make my day a lot better!

    Seriously though, if I could I would sit here thanking you all day for coming up with that answer. That just made me feel so much better.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by sgares View Post
    Woah, that was correct topsquark... thank you so much for that lol. I still have no idea why that is correct though, so if anyone could explain this to me that would make my day a lot better!

    Seriously though, if I could I would sit here thanking you all day for coming up with that answer. That just made me feel so much better.
    Do you see how the exponent of x^{2n} is going to be even since n\in\mathbb{N}?

    Well did you wonder what happened to the even terms?

    The reason is that if we let

    f(x)=\frac{1}{1+100x^2}

    and let f^{(n)}(0)

    We see that


    f^{(n)}(0)=\left\{ \begin{array}{cc} (-1)^n\cdot{10}^{2n} & \mbox{ if } {\text{n is even}}\\ 0 & \mbox{ if } {\text{n is odd}}\end{array}\right.

    So since two (three if excluding zero) of the first terms are odd numbers, we can see that they are zero.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,079
    Thanks
    375
    Awards
    1
    Another piece of advice. The problem asked you to find the Taylor series about x = 0. What Mathstud (and presumably you) derived was based on a geometric series summation. The two give identical answers, but if you did the actual work with the Taylor series you would have seen the coefficients that were 0 directly.

    That being said I would probably have given the same answer as you as such problems typically ask for only the non-zero coefficients.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Please help this problem is driving me crazy
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: January 30th 2010, 04:45 PM
  2. Out of 20 probelms two are driving me crazy.
    Posted in the Algebra Forum
    Replies: 8
    Last Post: October 29th 2009, 06:14 PM
  3. These Determinants are driving me crazy! (Matrices)
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 10th 2009, 06:44 PM
  4. This is driving me crazy!!!! LOGS!!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 14th 2008, 11:29 AM
  5. Problem with apples driving me crazy!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 5th 2005, 09:31 AM

Search Tags


/mathhelpforum @mathhelpforum