Formal definition for limit of a sequence | Series | AP Calculus BC | Khan Academy

A sequence is "converging" if its terms approach a specific value at infinity. This video is a more formal definition of what it means for a sequence to converge. Created by Sal Khan.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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[slavikchukhlebov]

Thank you. I spent many hours trying to figure out what epsilon and M meant in this context until I finally saw this. Without this video, I would still be totally lost. Thank you so much!

[dangerousangel]

I'm in advanced calculus now, doing pointwise and uniform convergence (sequences of functions) and REALLY.
This STILL HELPED ME.
Thank you very much! 😭

All semester long I've been wonder what he meant by n>N implies |an - l |<E ....
I now know.
I used to study/practice for Calculus II using your videos and it really helped me then....
Back then I'm sure I skipped over this video or didn't listen to it properly because I was like, "ah, delta/epsilon who cares? We never use this anyway" lol...
NOW WE'RE USING IT. 😭

[richardjimenez]

Thank you so much Khan!!!! This video let me understand what the limit of a sequence is in 4 minutes and my professors have days trying to make students understand. I wish these videos can be showed in lectures...

[shwethaathrady]

thank you so much for the video. actually i did not understand anything when my teacher taught me. now i understood it prety well

[vamsikrishnabodaballa]

I feel that Khan academy videos are very much understandable than any lectures I have attended.Thank you so much.🙏🙏🙏

[lightbikevids]

Replayed it 2 times before I finally understood thanks!!

[Mr_Catt_]

10 years later and this video continues being usiful to save our lives in university...thanku, finally understood this topic

[GS-tpvj]

Wow. What an explanation. Actually i m trying to understand this M hours and hours now i m clear about it. Thank u so much for this video.

[mlamba]

Thanks...struggled for half n hour to understand the same in Mich hoy's book

[kuldipkunghadkar]

One of the best explanation of a mathematical concept.

[tapurjoardar]

thank you so it is too helpfull... for this graphical representation

[alxnewman]

then you cant choose M to be 1, the point is that you can choose M to be whatever number you want as long as the condition is satisfied. so in your case M cannot be 1, it must be at least 2.

[linhthuongphi]

this is why i have tried my best to learn English!

[Mugwump]

Why do we even need the whole epsilon thing? Couldn't we just say that if for every M there is an n greater than M such that a sub n is closer to the limit than a sub M. The whole epsilon thing seems unnecessary. Is there a reason for it that I'm not seeing here?

[nugrahadethan]

Thanks a lot, this is really helping..

[Buciasda]

The condition is n>M. If M=1 then n has to be at least 3.

[shubhamprakash]

What a nice explaination !! my proofeesor wasn't able to make it clear even in 30 min.

[revathikankanala]

It's very helpful.... Thank you..

[pras]

Awesome explanation sir never under stood when my teacher taught r great😎😎😎

[aon]

Thanks for the video it was very helpful!