❖ Finding the Limit of a Sequence, 3 more examples ❖

Finding the Limit of a Sequence, 3 more examples, #1. Just another example of finding the limit of a sequence by taking a limit as n approaches infinity.
One often will encounter sequences in a Calculus course prior to dealing with Series. Make sure you can find limits of sequences as it will be an important skill to have when working with series.

#maths #sequence #series #limits #converge #convergent #diverge #diverges #divergent #pseries #exponential #rationalfunctions

[patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! Also, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly :)

[DrDrewsAdventures]

Your teaching style makes math so much easier to understand. I wish you had some videos on density and finding work. Physics applications with calculus is killing me right now. Thank you.

[haidernafees]

Patrick your videos are very helpful. I don't even have to study or take calculus 2 classes. Thanks for helping many of us in our math classes. I like it.

[bullterry]

man Patrick is my go-to guy when it comes to math. I usually go to his channel before I go to my teacher for help. Thanks dude!!

[iamloveandpeace]

I love youtube, especially these videos=THANK you so much!! 

[epicfailled]

I just passed my Analysis II class and maybe that, s because of you. Thank you sir you are a great teacher

[medishettykumar]

Sir.. i have one doubt actually why do we use limits in real sense?? like do we use to calculate where is the given function tending as the variable of the function is tending somewhere?? is it?? sir please reply!!

[azizk]

thank you, but it was extremely easy problems!

[thesituation]

Very helpful vid!
I'm from New Zealand and I always watch your vids, your making an impact all around the world man =)

[srsqtee]

Mr. Patrick, I'm taking calc II for the second time because I couldn't understand my previous professor.  Had I known you were looking out for people like me, I would have been fine.  Thank you very much!

[gethyc]

To show the last one we will use the sandwich theorem and the inequality(prove it by induction)

notice that 0<n^3/e^n <n/e^n <(by using the second inequality) n/2^n<(by using the first inequality) n/n^2= 1/n.

We had such a problem at our partial exam, to prove by definition of limits that (lim(n to infinity) n/3^n=0)) :)


Im sorry i could not reply at the video you asked the question on but it showed me an error. I hope this helps

[samyuktajadeja]

I LOVE YOUR VIDEOS. THEY HELPED ME W QUESTIONS I COULDN'T FIND ANYWHERE! PLEASE CONTINUE MAKING YOUR YOU CAN SAVE THE

[jasminejohnson]

thank u for this my math teacher made me feel dumb af

[moneymindsetmatrix]

Great Stuff Patrick, keep up the good work. 

From Australia

[gethyc]

That is true because sequences f(n) are defined with f:N=>R
but derivatives are used strictly at f:R => R

[NellyM]

i love your videos!! they are literally saving my life thanks!

[forstudy]

Really 12 years ago video
And still on top in helping😮😮

[bailey]

I don’t understand what you mean when you say “as n goes to infinity” is n an x value? i’m struggling to visualize it.

[IronsMedical]

Bro your changing the world and making life easier one youtube video at a time. It would be awesome if you made physics videos, with concepts as difficult as this, easy to understand.

[dexterdysthe]

I thought in order to use L'Hopitals rule the variable must be an element of the Real numbers? Because n is an element of the Natural numbers is it not required to compare the sequence to a function defined in terms of x such that x is an element of the reals?