Convergence of Series: Comparison vs. Limit Comparison Test

[squenshl]

Do I use the comparison test or limit comparison test to see if the series sin^2(1/n) converges or diverges and if the series n^2/(n^2+1) converges or diverges.

 

[sutupidmath]

for the first one i would use the comparison test, while for the second i would try the divergence test first, and see whether a_n-->0 as n-->infinity.

 

[squenshl]

Thought so, thanks.
For the first one I know a(n) = sin^2(1/n), so could I use b(n) = 1/(n^2).
As for the second I see that the limit as n tends to inf using the divergence test is 1/2 which doesn't equal 0 so therefore this series diverges. Thanks

 

[squenshl]

I have got no idea what test to use for the series lsin(n)l/n^2.
Any help.
And would I use a ratio test on the series n!/(2n+1).

 

[adriank]

Don't ask us if you would use so and so test on a series; try it yourself and see if it works.

For |sin n|/n², compare with 1/n².

 

[WMoor]

I just noticed that some of you are relying on these forums instead of attempting and working on the problems yourselves. This is a gentle warning that if by now you are unsure how to solve these problems, then you are not ready for the forthcoming test and your chances of doing well in Maths 250 would be small, and at best you would probably get a low grade. The purpose of assignments is to give you exercise in the concepts and skills discussed in lectures. The point is not to earn marks by any means possible; marks are a consequence of your understanding through practice.

Warren.

 

[sutupidmath]

Someone just got caught!Ops!...lol...

Well, while it is true that many students, including myself, ask for help in these forums, i would say that for the most part the people who seek for help here get only hints. THat is, it is them(with some exceptions) who do the most part of the job.