nth term test, divergence test, zero test (KristaKingMath)

Learn how to use the nth term test, aka divergence test, aka zero test, as a quick way to see whether a series diverges. Remember that this test tells you nothing about convergence. If the limit of the series is not equal to zero, then you can safely conclude that the series diverges, but you can't draw any additional conclusions. If the limit to the series is equal to zero, then the divergence test is inconclusive, and you have to use another test to determine convergence/divergence of the series.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[EM-duch]

broke it down really well thank you! God bless you!

[thetick]

Thank you, for this and your other videos.  Even when the math get complicated you use simple wording.  So many different professors use different "mathisms" it gets hard to understand.  

[jasonboynton]

Your saving my calc grade thank you so much 

[spencercampbell]

So for the third example if the second second term had been divergent would you say the overall function diverges? Or to put it another way wouldn't it be time effective to see if both parts get inconclusive results before trying to solve? Thanks for these videos their great

[ahmedaldakhoul]

very nice and good way to get solutions

[gaebi]

For a question similar to the last one, if one part diverges does the other automatically diverge

[SN]

Thanks for the awesome videos! I appreciate your help.

[kakarot-elbt]

Shouldn't the reminder be the SUM of a_n diverges if lim a_n is not equal to 0?

[minerofskies]

I have a similar natural log exercise in my Cal III class in which the limit actually goes to zero. The exercise however claims that the series is divergent (and therefore we must prove it). Which post-test (s) would you recommend for it? (I haven't taken calculus classes in a while so my memory is a bit fuzzy)

[jiangeyuan]

really like your video, really helps a lot!

[tenderscootch]

(3n+2)/(n+1).  the limit is 3.  my professor has this written in the notes as "converging", but since it is not equal to zero, shouldn't it diverge?

[tenderscootch]

also, is converging to a limit "converging"?  this is the language that I see used and I find it confusing.

[sanjay]

Krista but isnt this the same as convergence test?

[dpmike]

It’s a sequence, not a series a sub n

[MiloScheppie]

Krista, are you still single? (just asking for a friend of mine...)