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Math Help - String

  1. #1
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    String

    Find x of that x+2x^2+3x^3+4x^4+...=3, with |x|<1 and x \neq 0
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    What do you think is the correct answer and WHY?
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  3. #3
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    Question

    Quote Originally Posted by Apprentice123 View Post
    Find x of that x+2x^2+3x^3+4x^4+...=3, with |x|<1 and x \neq 0
    Does "find x of that" mean "find the values of x such that"...?
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  4. #4
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    Quote Originally Posted by stapel View Post
    Does "find x of that" mean "find the values of x such that"...?
    Yes
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  5. #5
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    x+2x^2+3x^3+4x^4+\cdots = \sum_{n=1}^{\infty} nx^n

    It can be shown that this is the power series for the function: f(x)= \frac{x}{(1-x)^2} \qquad |x| < 1
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