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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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\[\sum_{n=1}^{\infty} ((-1)^{n+1} x^n)/n \]
That's ln(1+x).
ln(1+1)=ln(2) but how you know it converges to this value?

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Other answers:

Alternating series test.
Are you familiar with Taylor Series or Maclaurin Series?
If you try to compute the Maclaurin series of:\[\ln(x+1)\]you will obtain the power series in your question.
differentiate the series...sun the then geometric series...integrate the series
*integrate the closed form after summing the geometric

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