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anonymous
 5 years ago
I have tried investigate the convergence/divergence of the following question, yet ended up with having it converging when it's supposed to converge:
an = (1)^n . (n+2)/(3n1)
anonymous
 5 years ago
I have tried investigate the convergence/divergence of the following question, yet ended up with having it converging when it's supposed to converge: an = (1)^n . (n+2)/(3n1)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, it will diverge. Although the limit as n approaches infinity has that (n+2)/(3n1) approaches 1/3, the (1)^n multiplier will have your limit oscillate...it won't be able to converge.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so because (1)^n diverges, by the theorem if one diverges all will diverge and therefore the sequence will diverge?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Kind of...in order for a sequence to converge, it must head toward a single value  that's the motivation for the definition. As you have that (1)^n thing attached, you won't have the case where you approach one value...you essentially approach two values: 1/3 and +1/3.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I've got it! Thank you.
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