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I am trying to find if this sequence is converging or diverging:

http://img9.imageshack.us/img9/623/72142860.gif [Broken]

Here is my work, but I highly doubt it because it is based on intuition:

http://img4.imageshack.us/img4/3589/54428513.gif [Broken]

Since the first limit diverges and the second limit is not equal to 0, then the sequence diverges.

Does anyone have a better, systematic way of dealing with this sequence and any other sign alternating sequence with (-1)^n

Thank you

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# Convergence/Divergence of this sequence

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