((2+(-1)^n)/n) converge or diverge?

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((2+(-1)^n)/n) converge or diverge?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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converge.
why?
I can't find a convergence test that is conclusive...Duke, what's your process?

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Other answers:

it's a geometric series.
sequence*
I used comparison test. Assume 1/n -> diverges and (-1)^n/n converges. ( This is a fact.) Your sequence just has a 2+ which can be dropped since +/- are meaningless. You can also use the alter series test.
*A alternating operator can turn sequence that normally diverge to converge.
Actually, you don't just have a 2+...you have a 2/n (which is divergent). Check your parentheses.. normally I'd agree with you completely, but it breaks down into 2/n + (-1)^n/n.
(2+((-1)^n))/n
Exactly. That fraction degrades into 2/n + ((-1)^n)/n.
We have to wait for the person to clear this up.
Sounds like a plan.

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