Ratio & Root Tests | Geometric Series Generalized

Series with a fixed ratio between all the terms were called Geometric Series. However, if there is not a fixed ratio, we can instead consider the limit of the ratios and look at that. This gives us a ratio test with conditions somewhat analogous to the Geometric Series. Similarly, in some instances it is better to look at the nth roots instead and then we get a so called Root Test.
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[@adamsusel3801]

That comparison to the r value in a geometric series just made it click for me! I've been looking for an explanation of why this works and now I get it, thank you!

[@alisavictory2969]

Agreed!

[@abdallahshariffu4603]

me too

[@maurocruz1824]

Your lectures left me clear that my english-listening level sucks, but fortunately mathematics is a universal language. Your way to explain things like these are unique. Thank you so much!

[@kiramsamy449]

this channel is a gem. thank you so much !

[@shanelindsay]

Just wanted to say I found your videos looking up stats/discrete math videos. Wanted to say thanks for all the uploads! you deserve so many more viewers. Keep making awesome videos man! you're a CS majors dream!

[@abbasbookwala]

Great ! Thank you very much. perfect analogy to bring about the intuitive feel

[@alisavictory2969]

Thank you very much! Very helpful. I like the connection to the geometric series! It clicked with me!

[@biggerthaninfinity7604]

Wow! Thank you for the best explanation that cleared up everything that I was having troubles with.

[@DrTrefor]

Glad it helped!

[@Ayesha_01257]

Very Well Explained 👍 with full enthusiasm ❤

[@jaimee8177]

Bc of coronavirus my two hour lecture has been replaced w this 9 minute video. Good explanation tho

[@Tferdz]

I never saw this analogy. Cool video

[@khloetran69]

Great video thank you

[@faoizashraf1027]

amazing teaching skills ...... lucky to have you : )

[@shamsadrahman]

For peeps who only want to watch the Root Test part, 6:40 - Root Test

[@jharnamandal2855]

Very nice video

[@biggerthaninfinity7604]

You’re a great teacher!

[@GrantGryczan]

Great intuitive explanation, relating these tests to the geometric series. Where did you get it from? Or did you come up with it yourself?

[@GrantGryczan]

@@DrTrefor Ha, alright then. Well it aint in my textbook

[@chawankonjela8627]

bravo🙌🙌

[@nuclearrambo3167]

I think 1 is inconclusive because there may be a horizontal asympote whose has height(y value) is not zero. I concluded that because if r value is 1 then there is no change in successive values of the serie then it will look like a horizontal asymptote. example: sigma sum from 1 to infinity ((1/x^2)+(1))

[@nuclearrambo3167]

In the other words it will behave like as if there is a infinitely long rectangle.

[@amirhussein3953]

Thank you for the explanation. Can you please show how sum(1/n) diverges? I think it should converge to 0

[@theleviathan3902]

You add them all up, the sequence goes to zero but if you add them all up it divereges

[@DamianWaynes]

Important note: the root test should have an absolute value inside the nth root!

[@dipsaha6178]

Sir I want the explanation of "the root test is more powerful than the
ratio test."

[@tonymunene1592]

But doesnt the series converge for r=1?? for the explanation at 0.42

[@umutyalcindag]

r=1 makes the series like a+a+a+a+… so it diverges

[@gardenmenuuu]

2:32 sir why is the third case inconclusive?Doesn't that imply that it is similar to geometric ratio with r=1,then it is too divergent?Please help

[@theleviathan3902]

That means that as you go to infinity, you end up getting closer to multiplying by 1 every single term, this could mean convergence or divergence since we have no other info

[@sirlewis3975]

i love you

[@Maria-yx4se]

sir you forgot to put absolute value for the root test

[@eduvazx]

Broo, the subtitles LMAOO

[@shanem3014]

the explanation of factorial algebra couldve been simpler

[@tokerrrre]

7.49 :)))))

[@amanjadnan8466]

Please go faster my teacher rich to chapter 11😥

[@endy_011]

amogus

[@nikobaka5272]

Literally every woman: (blah)^n