## Silenthill Group Title 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. 2 years ago 2 years ago

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1. Silenthill Group Title

$\sum_{n=1}^{\infty} ((-1)^{n+1} x^n)/n$

2. blockcolder Group Title

That's ln(1+x).

3. Silenthill Group Title

ln(1+1)=ln(2) but how you know it converges to this value?

4. blockcolder Group Title

Alternating series test.

5. joemath314159 Group Title

Are you familiar with Taylor Series or Maclaurin Series?

6. Silenthill Group Title

yes

7. joemath314159 Group Title

If you try to compute the Maclaurin series of:$\ln(x+1)$you will obtain the power series in your question.

8. Zarkon Group Title

differentiate the series...sun the then geometric series...integrate the series

9. Zarkon Group Title

*integrate the closed form after summing the geometric