Question

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

Answer 1

converge.

Answer 2

why?

Answer 3

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

Answer 4

it's a geometric series.

Answer 5

sequence*

Answer 6

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.

Answer 7

*A alternating operator can turn sequence that normally diverge to converge.

Answer 8

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.

Answer 9

(2+((-1)^n))/n

Answer 10

Exactly. That fraction degrades into 2/n + ((-1)^n)/n.

Answer 11

We have to wait for the person to clear this up.

Answer 12

Sounds like a plan.