Question

About convergence and divergence

Answer 1

I'll have my exam soon and usually they put the question about whether a series diverges/converges and stuff like that in the multiple choices. Now, usually I'm a bit slow on that but I'll need to be quick so I have more time on harder problems. So, does anyone have any tips or tricks to go over them faster? Like which test to go with first, which is more guaranteed to help you?

Answer 2

divergent is when your answer is infinity
convergence is a number as an answer

Answer 3

@marcelie yes, i know that. what i am asking is, is there anything that could help me finish with these numbers faster, because i never really know which test to use in which case, i end up trying all of then which is very time consuming and i dont have a lot of time on an exam.

Answer 4

hmm maybe know better the when you multiply the infinities

Answer 5

@marcelie thanks for the advice. :) helps so much!!

Answer 6

First and foremost, you'll need to know and be familiar with the various tests for convergence that your class or text has covered. Assuming you're at an AP-high-school level, these typically include the limit, ratio, root, comparison, and integral tests plus the test for alternating series, along with special types of series (e.g. geometric) that admit an immediate conclusion about their behavior.

Familiarity comes from repetition by doing practice problems. You'll start to see patterns that can help you make a sort of mnemonic device for yourself so you'll know when to implement a certain test. But there's more to it than that. You have to know *why* they work.

But, like I said, in practice when you're under a time crunch, looking for patterns is probably your best bet. There's only so many problems (allowing for minor variations) realistic enough to place on a test with the expectation that most get solved.