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(sqrt(2)/e^2)+(sqrt(2)/e^4)+(sqrt(2)/e^6)+(sqrt(2)/e^8)+...

 

Not sure if I started it out correctly, but I turned it into a geometric series:

infinity ∑ n=1 (sqrt(2)/e^2)^n

 

a=1 & r = (sqrt(2)/e^2)

 

& if I'm right if |r| < 1, then it's convergent. If |r| ≥ 1.

Guest May 3, 2017
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2+0 Answers

 #1
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The sqrt(2) doesn't increase in power term by term, (i.e it stays at sqrt(2) for each term).

Remove it as a common fact and what is left is a GP.

Guest May 3, 2017
 #2
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The series should converge to: sqrt(2)/((e - 1) (1 + e)) = ~0.221349373.....etc.

Guest May 3, 2017

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