Regarding convergence: Sometimes it is that easy as it looks like and sometimes it just seems to be easy but it is not and one has to make some...

Regarding convergence:

Sometimes it is that easy as it looks like and sometimes it just seems to be easy but it is not and one has to make some rearrangements to obtain the correct answer.

My question: How do I know whether a series is that simple or whether a series needs some rearrangements.

For instance: lim n->infinity 1 - n^2

my first thought was the answer is -infinity, then I thought maybe too simple and I divided everything by n^2. That is allowed, isn`t it?

Than I have lim n-> infinity (1/(n^2) - 1

As 1/n^2 converges to zero I would have left -1, i.e. the series would then converge.

I know that this series diverges but very often one has to generate fractions.

Do you have some documents that discuss this problem or can you give me the answer?

Thank you.