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.