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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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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[adamsusel]

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!

[maurocruz]

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!

[biggerthaninfinity]

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

[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!

[jaimee]

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

[Ayesha_]

Very Well Explained 👍 with full enthusiasm ❤

[alisavictory]

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

[shamsadrahman]

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

[kiramsamy]

this channel is a gem. thank you so much !

[abbasbookwala]

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

[nuclearrambo]

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))

[faoizashraf]

amazing teaching skills lucky to have you : )

[amirhussein]

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

[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?

[dipsaha]

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

[DamianWaynes]

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

[Maria-yxse]

sir you forgot to put absolute value for the root test

[tonymunene]

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

[shanem]

the explanation of factorial algebra couldve been simpler

[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