Question

Can someone help me with this sequence problem?
http://dl.dropbox.com/u/6717478/Untitled.png

I was thinking of using the squeeze theorem to help show the limit doesn't exist

Answer 1

You can just see that the absolute value of the sequence converges at 1, so with (-1)^(n+1) it will oscillate infinitely

Answer 2

how does showing that the absolute value of the sequence converging at 1 help show that the original sequence doesn't converge?

Answer 3

Because you know that (-1)^n oscillate

Answer 4

I know that (-1)^n oscillates, but sequences that oscillate can still converge

Answer 5

if the absolute value one converges doesn't the other one converge too?

Answer 6

but trying ratio test...but that is slow goin

Answer 7

It converges if the absolute value is infinitesimal(i'm not english, I mean that will become 0), but in this case it's 1! In the limit solution will be: 1, -1, 1, -1, 1, -1, 1, -1, 1, -1...

Answer 8

I think my squeeze theorem method is working
I'm showing that
-n <= (-1)^n+1 <= n
-------- -------- --------
n+sqrt(n) n+sqrt(n) n+sqrt(n)

and the outer 2 limits go to -1 and 1 so the middle limit doesn't exist

I think this works

Answer 9

I think this is what you meant by the absolute value part too right?

Answer 10

You're right, also with the squeeze method(in Italy we called it "Teorema dei carabinieri" XD) it is demonstrate

Answer 11

ok, that makes sense. Thank you for your help :)

Answer 12

ah i get it...absolute convergence test won't work because when the answer is one...cannot draw any conclusion...