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anonymous

  • 5 years ago

How to solve: Use geometric series 1/(x+1) = Summation (n=0 to infinity) (-1)^n * x^n, to find the power series representation of f(x) = 1 / (4x +3).

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  1. anonymous
    • 5 years ago
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    F(x)=1/(x+1) can be represented as \[\sum_{0}^{infiniti}(-1)^n x^n\] F(x)=1/(4/3x +1) is same as f(x)=1/4x+3 So you would substitute in 4/3x in place of x

  2. anonymous
    • 5 years ago
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    Does it at least make some sense?

  3. anonymous
    • 5 years ago
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    You would have to multiply the summation by 3.

  4. anonymous
    • 5 years ago
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    1/3(4/3x+1) you can factor out 1/3

  5. anonymous
    • 5 years ago
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    * actually 1/3

  6. anonymous
    • 5 years ago
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    Yes you factor out the 1/3 but you did not account for it.

  7. anonymous
    • 5 years ago
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    I missed that

  8. anonymous
    • 5 years ago
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    it is one of those little errors.

  9. anonymous
    • 5 years ago
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    So Does it make sense now WRosa?

  10. anonymous
    • 5 years ago
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    \[1/3\sum_{0}^{\infty} (-1^n)(4/3x)^n\]

  11. anonymous
    • 5 years ago
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    So the solution is: f(x) = 1/(4x+3) f(x) = 1/3 ((4/3)x + 1) \[1/3 \sum_{n=0}^{\infty} (-1)^{n} ((4/3)x)^{n}\]

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