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 Divergent or Convergent??

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Is the following series convergent or divergent? And, if covergent, what is the result or the answer?

1 - 1/2 + 1/3 - 1/4 + 1/5.........to infinity. Thanks for any help.

 Jul 24, 2016

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 #2
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This is a famous series that has been known for a long time. It converges extremely slowly (evaluating the first 10,000 terms gives 3 accurate digits)!!. It converges to ln(2)=0.69314718055......etc.

 Jul 24, 2016

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 #1
avatar+128656 
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See if this helps :

 

https://www.wolframalpha.com/input/?i=1%2F%5B2n-1%5D-1%2F%5B2n%5D++sum+1+to+infinity

 

 

 

cool cool cool

 Jul 24, 2016
 #2
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Best Answer

This is a famous series that has been known for a long time. It converges extremely slowly (evaluating the first 10,000 terms gives 3 accurate digits)!!. It converges to ln(2)=0.69314718055......etc.

Guest Jul 24, 2016

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