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anonymous
 5 years ago
does this converge or diverge sigma n=1 to infinity 1/n^2 tan 1/n
anonymous
 5 years ago
does this converge or diverge sigma n=1 to infinity 1/n^2 tan 1/n

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmm, this is a tough one. going to have to bust out my calc resources =)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0check out this resource: http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can use the squeeze theorem here , now we have the following:\[\sum_{n=1}^{\infty} \frac{\tan(\frac{1}{n})}{n^2}\] So by squeeze theorem we have : \[\frac{\pi}{2} < \tan \frac{1}{n} < \frac{\pi}{2}\] divide by n^2 both sides and you'll get : \[\lim_{x \rightarrow \infty}\frac{\pi}{2n^2} <\lim_{x \rightarrow \infty} \tan \frac{1}{n} <\lim_{x \rightarrow \infty} \frac{\pi}{2n^2}\] where : \[\lim_{x \rightarrow \infty} \frac{\pi}{2n^2} = \lim_{x \rightarrow \infty} \frac{\pi}{2n^2} = \lim_{x \rightarrow \infty} \tan \frac{1}{n} = 0\] where series = a finite number = 0, then it converges, correct me if I'm wrong ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wow, great answer! medal'd

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but please check if there's any mistake :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can u please explain why tan of 1/n is b/w pi/2 and pi/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first, graph tan (n) on paper, you'll notice that tan (whateve angle it has here) is between pi/2 and pi/2 :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you sketch all tans on the graph, then you'll see different intervals that you can take ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0other thatn pi/2 and pi/2, depends on the tan that you want to choose, but I chose the simplest of all lol :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and how did u got from the inequality sign to the equal sign

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I didn't , I just applied the sqeeze theorem and wrote it down :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which says if limit of (a) as x >infinity = 0 and limit of (b) as x> infinity = 0 then limit of (c, the one that's in the middle) = 0 ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0pi/2 = a and pi/2 = b, so c = tan(1/n) ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0u guys are brilliant in math ...........;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0np ^_^ lol sath, I wasn't at all, but I worked hard to reach this level :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha u all are deserving student .....best of luck..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you, likewise :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0am the student of medicine but only becauz of some iq question am here.....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you an expert at writng

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0want to do a google doc \
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