Limits and Sequences

http://img215.imageshack.us/img215/8624/limitscz6.jpg [Broken]

That's the question and the answer.

I don't get why it converges to -1/2 and how you can tell just by looking. Maybe I'm not understanding well enough but I understand how to find the limit, just I thought the limit to infinity showed that 0 was what it converged to, not -1/2.

Any help? Thanks.

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