I am currently trying to find when series converge or diverge. I am learning this form a text with very little input from a prof (online classes) It seems that there is alot of personal technique in determining convergence. The book gives a few theorems, which I understand. But knowing which function to choose for comparison and manipulation inorder to use these theorems is not explained in the text. From looking at the study guide it appears there are multiple ways to arrive at the answer, and it may have to do with personal preference.
So my question is this. What are your steps that you like to use to determine conv./diver. Multiple answers would be welcome as it seems this might have some basis in personal choice.
Personally I always go with the ratio test. Normally I try and figure out before i've done the calculation if it's going to work or not!
If that one fails, I try the sandwich test. This does require a knowledge of which series converge and which series diverge in the first place!!(Giggle)
The sandwich test is particularly useful for situations involving cos and sin. For example:
and we all know that converges to .
Are there any series in particular that you're having trouble with?
None particular, all in general. I haver been doing ok so far in calc2 but I feel like I was just dropped into brain surgery with a high school ed. when it comes to series. Not much guidance in the text when it comes to using the theorems.