Question

what is the difference between the test for divergence and the integral test?

Answer 1

The integral test can be used to test if a function is either convergent or divergent depending on your results. the Test for divergence can only be used to test if a function is divergent and if it fails tells you absolutely nothing about your function.

Answer 2

I'm just making sure here: the test for divergence tells you if a series is divergent but it "tells you absolutely nothing about your function"?

Answer 3

if it fails. if the test for divergence is valid i.e. meets all requirements to pass \[\lim_{a \rightarrow \infty}f(x)=0\] or if same limit does not exist then the function is divergent. if the limit does exist, then you will have to try another test to see if it is convergent or divergent.

Answer 4

I see. Thank you.

It seems like I'll rarely see the test for divergence on the exam. Is that typical?

Answer 5

I meant I would be in a situation in which I must use the test for divergence because nothing else would work.

Answer 6

possibly. on my exams i always did this one first because its quick and easy. and if it didnt work out its not too much time lost. so its nice.

Answer 7

thank you for your help.

Answer 8

no problemo. glad to help