anonymous
  • anonymous
does this converge or diverge sigma n=1 to infinity 1/n^2 tan 1/n
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
hmm, this is a tough one. going to have to bust out my calc resources =)
anonymous
  • anonymous
check out this resource: http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx
anonymous
  • anonymous
you 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 ^_^

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anonymous
  • anonymous
wow, great answer! medal'd
anonymous
  • anonymous
lol, thank you ^_^
anonymous
  • anonymous
but please check if there's any mistake :)
anonymous
  • anonymous
can u please explain why tan of 1/n is b/w -pi/2 and pi/2
anonymous
  • anonymous
first, graph tan (n) on paper, you'll notice that tan (whateve angle it has here) is between -pi/2 and pi/2 :)
anonymous
  • anonymous
k
anonymous
  • anonymous
if you sketch all tans on the graph, then you'll see different intervals that you can take ^_^
anonymous
  • anonymous
other thatn -pi/2 and pi/2, depends on the tan that you want to choose, but I chose the simplest of all lol :)
anonymous
  • anonymous
and how did u got from the inequality sign to the equal sign
anonymous
  • anonymous
I didn't , I just applied the sqeeze theorem and wrote it down :)
anonymous
  • anonymous
which 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
  • anonymous
-pi/2 = a and pi/2 = b, so c = tan(1/n) ^_^
anonymous
  • anonymous
k ty u for help
anonymous
  • anonymous
u guys are brilliant in math ...........;)
anonymous
  • anonymous
np ^_^ lol sath, I wasn't at all, but I worked hard to reach this level :)
anonymous
  • anonymous
haha u all are deserving student .....best of luck..
anonymous
  • anonymous
thank you, likewise :)
anonymous
  • anonymous
am the student of medicine but only becauz of some iq question am here.....
anonymous
  • anonymous
are you an expert at writng
anonymous
  • anonymous
want to do a google doc \

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