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Does the series arctan n converge? 
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#1
Mar111, 02:28 PM

P: 42

I'm sure it doesn't, but how do I find out?
[tex]\sum^{infinity}_{n=1} arctan (n)[/tex] I thought about using the integral test, but it's not decreasing. Any hints? Could I somehow use proof by induction to show that its an increasing function? 


#2
Mar111, 03:11 PM

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P: 18,346

What is [tex]\lim_{n\rightarrow +\infty}{arctan(n)}[/tex]?? Does this tell you something about convergence?



#3
Mar111, 03:28 PM

P: 42

pi/2, so by the test for divergence it must diverge! Ohh



#4
Mar111, 03:33 PM

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P: 18,346

Does the series arctan n converge?
Correct!! A good advice: Always apply the test for divergence first!!



#5
Mar111, 03:34 PM

P: 42

Thanks :)



#6
Mar111, 08:41 PM

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P: 21,397




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