Question

To test the convergence of series sin(9/n), which test should i use?

Answer 1

I think that the partial sum test will give you a sufficient answer. As n increases, the value of sin being evaluated gets increasingly smaller after n = 9. Then looking at even larger values, the sin function approaches the smaller and smaller values getting closer to the sin(0) = 0 . This means that it converges to zero.

Answer 2

My bad, there is another name for that, but the behavior follows the explanation. Now as to the sum, of the series, that's a different story.

Answer 3

thanks for helping out. you used the nth term test or whatever it is called, it is a test for divergence

Answer 4

yeah, that stuff drives me nuts because it's so cool, but there are so many forms and rules, and only a few things I actaully need to know how to use. Hard to remember all of it.