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Silenthill
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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.
 2 years ago
 2 years ago
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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Silenthill Group TitleBest ResponseYou've already chosen the best response.0
\[\sum_{n=1}^{\infty} ((1)^{n+1} x^n)/n \]
 2 years ago

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
That's ln(1+x).
 2 years ago

Silenthill Group TitleBest ResponseYou've already chosen the best response.0
ln(1+1)=ln(2) but how you know it converges to this value?
 2 years ago

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
Alternating series test.
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.0
Are you familiar with Taylor Series or Maclaurin Series?
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.0
If you try to compute the Maclaurin series of:\[\ln(x+1)\]you will obtain the power series in your question.
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
differentiate the series...sun the then geometric series...integrate the series
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
*integrate the closed form after summing the geometric
 2 years ago
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