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Math Help - power series representation.

  1. #1
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    power series representation.

    a. need to differentiate 1/(1+x)^2 to find power series representation and the radius of convergence. (think that is the quotient rule)

    (....= -2x/(1+x)^4 ??)

    b. use part a to find power series 1/(1+x)^3

    c. then use b to find power series for x^2/(1+x)^3


    please help for this one, i'm confused throughout the entire problem.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rcmango View Post
    a. need to differentiate 1/(1+x)^2 to find power series representation and the radius of convergence. (think that is the quotient rule)

    (....= -2x/(1+x)^4 ??)
    um, the quotient rule is overkill. note that you have (1 + x)^{-2} so the derivative is -2(1 + x)^{-3} = \frac {-2}{(1 + x)^3}

    ...i think you ate part of the question. the question probably said something to do with the second part of my hint for part (b)

    b. use part a to find power series 1/(1+x)^3
    Hint: find the power series of \frac 1{(1 + x)^2} first. then differentiate the formula. you should be able to take it from there.

    you can find the power series for \frac 1{(1 + x)^2} by differentiating the formula for the power series of \frac {-1}{1 + x}...which you can find quite easily by considering the power series for \frac 1{1 - x} ...something you should know by heart

    c. then use b to find power series for x^2/(1+x)^3
    multiply your answer in part (b) by x^2
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