Which test should I use for the series tan(1/n)
Favorites|Homepage
Subscriptions | sitemap
HOME > > Which test should I use for the series tan(1/n)

Which test should I use for the series tan(1/n)

[From: ] [author: ] [Date: 11-12-12] [Hit: ]
infinity).Root test doesnt look like an option, and I dont think the Limit Comparison test will help, because the form will be: tan(1/(1+x))/tan(1/x) since I dont know what I would do with that.So I ran out of tests, and there has to be a way.......
Test the series for convergence or divergence.

Sum from 1 to infinity of tan(1/n)

Test for Divergence doesn't work, since we have tan(1/n) = 0.

I've considered the integral test, but the related function f(x) = tan(1/x) is discontinuous on the interval [1, infinity).

Root test doesn't look like an option, and I don't think the Limit Comparison test will help, because the form will be: tan(1/(1+x))/tan(1/x) since I don't know what I would do with that.

So I ran out of tests, and there has to be a way. Can anybody please help me?

Thank you.

-
Use the limit comparison test with the harmonic series.
lim(n→∞) tan(1/n) / (1/n)
= lim(n→∞) (-1/n^2) sec^2(1/n) / (-1/n^2), by L'Hopital's Rule
= lim(n→∞) sec^2(1/n)
= sec^2(0)
= 1.

Since the harmonic series diverges, so does the series in question.

I hope this helps!
1
keywords: test,use,series,should,for,tan,the,Which,Which test should I use for the series tan(1/n)
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .