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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] use the graph of the sequence to decide whether the sequence converges or diverges. then verify your result analytically

[00:00:07] hello!

Brian M (Tutor)

[00:00:12] hi and welcome to tutor.com !

Guest (Customer)

[00:00:19] thanks!

[00:00:21] how are you>

[00:00:22] ?

Brian M (Tutor)

[00:00:28] Great thanks for asking!

Guest (Customer)

[00:00:33] no problem!

Brian M (Tutor)

[00:00:35] How are you?

Guest (Customer)

[00:00:40] pretty good, thanks!

Brian M (Tutor)

[00:00:49] Would you be able to show me either the graph or the formula for your sequence?

Guest (Customer)

[00:00:54] i can show you both!

Brian M (Tutor)

[00:00:59] Awesome1

Guest (Customer)

[00:00:59] hold on a moment

Brian M (Tutor)

[00:01:30] Sure thing

[00:03:32] Okay so what does your intuition tell you about this. Converge or diverge?

Guest (Customer)

[00:03:54] well what axis am i looking at

[00:03:56] ?

Brian M (Tutor)

[00:04:11] Well it should converge to a single y value

Guest (Customer)

[00:04:11] oh i guess this might be
helpful...

[00:04:57] hmmm

Brian M (Tutor)

[00:05:19] So does that seem to be getting close to any particular y value?

Guest (Customer)

[00:05:50] hmm y value? not sureeee

[00:05:57] it goes between 1 and 3

Brian M (Tutor)

[00:06:10] Right it just keeps hopping back and forth

[00:06:20] NOt really deciding on one particular value, so the answer is no

Guest (Customer)

[00:06:31] okay

Brian M (Tutor)

[00:06:36] So it will.....?

Guest (Customer)

[00:06:49] converge......

Brian M (Tutor)

[00:07:11] Well it DOESN'T settle on a y value to converge to, so it must .....?

Guest (Customer)

[00:07:17] diverge?

Brian M (Tutor)

[00:07:23] Right!

[00:07:34] Diverge doesn't mean blows up to infinity, Not all the time

Guest (Customer)

[00:07:42] gotcha

Brian M (Tutor)

[00:07:43] Sometimes it just means it cant settle on one numbers

[00:08:17] Alright so now let's see how we can prove it will the equations. Any ideas?

Guest (Customer)

[00:08:39] this is what i don't understand
actually

Brian M (Tutor)

[00:08:48] That's fine

Guest (Customer)

[00:08:47] we have to show the limits
though, right?

Brian M (Tutor)

[00:08:51] right

Guest (Customer)

[00:08:57] okay so

Brian M (Tutor)

[00:09:10] give it a go adn I will watch and correct anything you might do wrong

Guest (Customer)

[00:09:39] hmm

Brian M (Tutor)

[00:10:03] Yeah see it is kinda hard because we can't tell what hat -1 does right?

Guest (Customer)

[00:10:23] right

Brian M (Tutor)

[00:11:02] So here is a trick, since all the even n's are the same as far as that 1 is concerned and all the odds ones are the same, we can split this into 2 limits

[00:11:24] ANNNNND if the two are equal to each other, then it converges

Guest (Customer)

[00:11:21] okay

Brian M (Tutor)

[00:11:28] If not, it diverges

Guest (Customer)

[00:11:42] okay

Brian M (Tutor)

[00:12:24] So what is the limit as n approaches infinity if all the n's are even?

Guest (Customer)

[00:13:05] they are positive

Brian M (Tutor)

[00:13:31] Right so they are all 1's

[00:13:42] What about the odds

Guest (Customer)

[00:13:49] negatives

Brian M (Tutor)

[00:14:10] Right! And are the two limits the same?

Guest (Customer)

[00:14:29] no

Brian M (Tutor)

[00:14:40] That mean's the odds and even n's can't decide on a value, so it does not converge, so we say it diverges!

[00:14:43] SO you proved it!

Guest (Customer)

[00:14:49] yay

[00:14:52] it seems weird though

[00:14:57] i wouldn't have known to do
that

Brian M (Tutor)

[00:15:04] Yeah it is pretty weird.

[00:15:13] There are other ways but this is the easiest

[00:15:17] It is a cool trick though

Guest (Customer)

[00:15:34] agreed haha

[00:15:35] thanks!

Brian M (Tutor)

[00:15:54] No Problem! Any questions about what we did?

Guest (Customer)

[00:16:10] nope!

[00:16:13] i think i get it

Brian M (Tutor)

[00:16:17] Awesome! Well then thank you very much, you were a great student! Please take a minute to fill out the survey on your way out and have a great day!

Guest (Customer)

[00:16:21] stll weird but that's okay

[00:16:22] haha

[00:16:26] you too!

[00:16:28] thanks! :]

Brian M (Tutor)

[00:16:32] Thanks!

[00:16:34] Bye!