Yes, that is correct. The terms must go to zero in order for a series to converge. You should try this test first when faced with a series.
Face with the series;
Sum from n=1 to infinity of: n/(1+n),
And i'm asked to use any relevant tests and then determine if it converges or not.
I used the ratio test and got it to =1 therefore inconclusive, root test doesnt seem applicable, can't use integral test as the function is not decreasing, is all that correct and is what i've done below correct,
lim (as n --> inf) (n/(1+n)) is 1 as co-efficients of two greatest growing terms are 1/1, as limit doesn't equal 0 the series is divergent.
I'm really unsure with this stuff applying the tests seems simple but the text i have is very shady on how to otherwise deal with the series.
Any help would be GREATLY appreciated.