Convergence/Divergence of this sequence

fishingspree2

Hello,

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



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

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

tiny-tim

Hello fishingspree2!
Do you mean the sum, ∑ of that?

Hint: try subtracting one term from the next … that'll give you a sum of positive terms.

fishingspree2

hello

no i didn't mean the sum of that
i meant sequences like explained on http://tutorial.math.lamar.edu/Class...Sequences.aspx

tiny-tim

oooh sorry …

i was confused by the square brackets

(i wish the latex was back )

in that case …
Why do you doubt it … that's fine!

Just tune it slightly by saying that the even terms converge to 2, and the odd terms converge to -2, so clearly it has no limit.

fishingspree2

thank you tiny-tim :)