Convergence or Divergence of a Series with Sinusoidal General Term

[the_storm]

Homework Statement

a_n = sum of n * sin(\frac{1}{n} )from n =1 to n =infinity

Homework Equations

Test the series for convergence or divergence

The Attempt at a Solution

I tried the comparison test with b_n = sum of n but it fails because a_n < b_n
which means a series smaller than a divergent series and this gives me no information about the a_n ... I tried also the integral test but I couldn't do the integration ... so what do u think guys ?

 

[Dembadon]

Try the Nth Term Test.

Hint: Without doing the test, you can see that you'd be adding 1 forever...

 

[the_storm]

check the problem again

 

[SVXX]

It's not nice to change the question when the expert isn't looking...

Hence by Cauchy's Fundamental test for Divergence, as the limit is not zero, the series diverges. (http://www.math.oregonstate.edu/hom...StudyGuides/SandS/SeriesTests/divergence.html)

 

[Dembadon]

Since this isn't an alternating series, does the general term go to zero as n goes to infinity?

Edit: Didn't see SVXX's post before I replied.