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Silenthill

  • 3 years ago

Find the sum of the series and explain how you know the sum converges to this value. Sum of (((-1)^(n+1))/n) n=1, infinty.

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  1. Silenthill
    • 3 years ago
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    \[\sum_{n=1}^{\infty} ((-1)^{n+1} x^n)/n \]

  2. blockcolder
    • 3 years ago
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    That's ln(1+x).

  3. Silenthill
    • 3 years ago
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    ln(1+1)=ln(2) but how you know it converges to this value?

  4. blockcolder
    • 3 years ago
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    Alternating series test.

  5. joemath314159
    • 3 years ago
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    Are you familiar with Taylor Series or Maclaurin Series?

  6. Silenthill
    • 3 years ago
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    yes

  7. joemath314159
    • 3 years ago
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    If you try to compute the Maclaurin series of:\[\ln(x+1)\]you will obtain the power series in your question.

  8. Zarkon
    • 3 years ago
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    differentiate the series...sun the then geometric series...integrate the series

  9. Zarkon
    • 3 years ago
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    *integrate the closed form after summing the geometric

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