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

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

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

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

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

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

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