Post #9

Well does it converge or diverge?

You should probably try the nth term test before trying another method.

P-Series: n^p
if p is greater than 1-->converge
if less than or eqaul to 1-->diverge

Geometric: (1/2)^n
if the absoultue value of r(which is the n) is less than 1-->converge
if the absoultue value of r greater than 1-->diverge

Intergral Test: Probably use when everything fails.
First, take the limit from 0 to infinity.
Second, integrate like normal.
Third, plug in 0 and infinity.
Finally, take the limit.

If you still get any form of infinity-->diverge
if you get a number-->converge.

Comparing: You can compare the problem to an eaiser one.
1. direct comparison
2. limit comparison


My Question: I need someone to explain the difference between direct and limit (the steps and everything). I'm afraid that I'm mixing them up or using a combination of both. Please help.

A blog

So steph came to me and asked me how to break down the steps for finding whether or not a series converges or diverges. So...I believe they're the following...

1. nth term test-so basically you're going to just take the limit as n goes to infinity right off the bat...if it equals something other than zero, you know for sure that it diverges. However, If you get 0, you have to proceed to next step...

2. Okay. for step two you can choose between a, b, and c.
a. p series
b. geometric
c. integral test

**basically, you have to recognize that if it's 1/n^(exp), it's a pseries. If not you see if it's geometric (i.e. something raised to the n). And if it's something that looks easy to integrate, integrate it.

If step 2 fails, go onto step 3.

3. Unless the problem tells you otherwise, you can use either direct comparison OR limit comparison. For direct, you just compare it to something bigger (so if i have a fraction, the number on the bottom will be smaller...I know, confusing...). So once I find something bigger and similar, I just go through step 2. Same goes for limit comparison test, although, all you need is something similar, doesn't have to be either bigger or smaller than the original. Then all you do is take the limit as n goes to infinity.

simple enough??

I know it's confusing, you just have to think through all the steps.


QUESTIONS:

I have NO CLUE WHATSOEVER how to determine if a test is "inconclusive". So if you have that practice packet, problem 16...I got the integral test done, but I got infinity minus something. Does that mean it's inconclusive??? kbye.

post 9

so, still confused with chapter 9 stuff..
i'll just go over what i know.
so if you are given something, (idk if it matters if it is a sequence or a series).. you automaticaly take the nth term test.
so take lim as n goes to infinty. if you get 0, you have to move on to take another test. if not, it automatically diverges. the next tests are:
geometric, p-series, or integral teset.
nowwww, i know geometric is when you have an exponent, and p-series is when you haev a fraction. that's about all i know. therefore idk how to choose one, what to do after i choose one, or anything like that. i'm just so lost, idk why. i've been having a bad past few weeks.

anything else that i didn't mention in here, please explain to me. i think i need a tutor for this chapter or something.. idk.

I DO NOT UNDERSTAND:
direct comparison test
limit comparison test
^^i completely failed that quiz. ha

Ryan - October 24 Post

To be honest, I really have been lost since we started this chapter. It's probably because I didn't do my homework the first night, and I've never been able to catch up. So I'll start where I started to get lost (9.1).

*Sequence - a list of numbers.

*To find the terms in a sequence, simply plug in n (the term you are on) for x and solve.

*Sequences converge if they have a limit.
*Sequences diverge if they don't have a limit.
*To determine if a sequnce has a limit, take the limit as n->infinity of a(sub)n.

******Something we need to know!!!!!!!!
Limit(as n goes to infinity) of (1+(1/n))^n = e

*Sequence properties follow limit properties.

**Sqeeze Theorem.
- <= an <= +
*For sequences - sqeeze with a convergent sequence related to a(sub)n.

*Monotonic - if terms are always increasing or always decreasing.

*If a sequence is:
*bounded and monotonic - it converges
*bounded and not monotonic - it diverges
*not bounded and monotonic - it diverges

Post #9

So, blogger is finally accepting my password and I can now do my blog the right way! Yayy!

So, this week, on the days I was here, we reviewed and took some quizzes.

I will explain, to the best of my knowledge of how to tell if something converges or diverges.

So, first things first you shoud check if it's geometric. Geometric is when something is being multiplied to every term in the series. If the thing that is getting multiplied to is less than one, the series CONVERGES.

Next, is alot like geometric..P-Series. Its p-series if you have a fraction and the bottom is n raised to the number exponent. If your number is less than or equal to one it DIVERGES, if its greater than one it CONVERGES.

Now, lets go over the limit comparison test, you take an equaiton and simplify it by taking the greatest exponent terms and taking the limit of that...

HERE COMES MY QUESTION: WHAT DOES THIS TELL YOUUUUUU?

I have the same question for Direct Comparison Test along with the integral test.

Can anyone tell me how these three tests give you an answer..and how do you know if it doesn't help you?