Ratio Test Part 1 Simplifying Factorial and Exponential Ratios

This is the first of two videos. In this video, I state the Ratio Test, explain that it is used for expressions involvinv Factorials and Exponential Expressions, and then talk about how certain complicated factorial and exponential expressions are simplified. I apply the Principle of Mathematical Induction to show one equality.

[adolphfrederic]

Adolph Frederic
MAC2312
From 1:00 to 3:50
One new concept I learned from this video is the true meaning of the term factorial.

[Vooovo-cv]

Xilai Jin
MAC2311
One new concept I learned from this video was inconclusive can occur in a ratio test when the limit is equal to 1.

[sheercold]

Robert Rosario
MAC2312

Hello Professor Hearn! This video helped me understand how factorials work and what applications they can be used for, as prior to this I had never really had to work with them.

[madbggyhat]

Tobias Grant
MAC2312
I finally understood that (n+1)!/n! = n! since (n+1)! is ONE more then n! algebraically. Reviewing it, I'm able to connect that the Root test is used for eliminating Factorials from the series so that we are left with a more simpler form of the series to eveualuate the divergence/convergence.

[imanismith]

Imani Smith
Mac2312
I learned that converges absolutely mean the series itself and the series of absolute value both converge.

[edisondelmoral]

Edison Del Moral
MAC2312
One concept I learned from this video is that when dealing with factorials in fractions, it's best to expand them a bit to see what cancels out and what is left over. From there it's possible to simplify and produce a final answer with the terms that don't cancel.

[luisalejandrovenegasgonzal]

Luis Venegas
MAC2312
I learned how to simplify complex factorials from this video

[radneygustave]

Radney Gustave
MAC2312
An insight I gained from watching video was how to really use and having a better understand of factorials. Also it helped me what I would need to look for when using the Ratio test.

[ashleyandrade]

Ashley Oliveira
MAC 2312

One thing to take away from this video is that the ratio test is similar to the root test but it is very beneficial to use this test when working with factorials and exponential functions.

[adamini]

Adam Minieri
MAC2312
One take-away from this video is by using the principal of mathematical induction if k=n we can also say that the equality holds for k=n+1

[romariobillings]

Romario Billings
MAC2311
I learned from this Video that a series converges absolutely when both the absolute value of a term and the term from the series converges.

[justinmyrick]

Justin Myrick
MAC 2312
One takeaway from this video is how to simplify factorial expressions. This will help me when expanding expressions for the ratio test. It also helped hearing the conditions for which the ratio test converges, diverges, or is inconclusive.

[NgocNguyen-sudh]

Ngoc Nguyen
MAC2312
In this video, I learned that the ratio test is a test for the convergence of series. The series converges absolutely if the limit of the ratio of the terms as n approaches infinity is less than 1. The series diverges if the limit is greater than 1 or equal to infinity. The test is inconclusive if the limit equals 1.

[braulioqb]

Braulio Quintana
MAC2312
My take-away from this video is that the ratio test is helpful with factorial and exponential functions in order to finds ints convergence or divergence. I also learned that when you have an n! you need to subtract the one to the n and if inside of a parenthesis then you can use distributive property.

[LexiMooniee]

Alexia Laylor
MAC2312
One new concept that I learned from this video was that the ratio test can come in handy when handling factorial and exponential functions. Also that by the ratio test, a series will converge absolutely if the limit is less than one, and diverges if the limit it greater than one or equal to infinity. It would inconclusive if the limit equals one.

[davidelepri]

Davide Lepri
MAC2312
In this video I learned how to manipulate and solve complex factorials. The explanation was very clear, thank you so much!

[madison]

Madison H
MAC2312
One takeaway from this video is that if the ratio test leads you to an answer of 1, you probably should look for other tests to use because a limit of 1 means the ratio test was inconclusive.

[johninturias]

John Inturias
MAC2312
One new concept I learned from this video was how to solve complex factorials

[andreadorbessan]

Andrea Dorbessan
MAC 2312 T-T
in this video I learned the ratio test it is helpful with factorial and exponential functions

[fabiolahilewsky]

Fabiola Hilewsky
mac2312
In this video I learned how to used factorials and exponential expressions and how they could be simplified.