I could've gotten this information in 135 minutes-worth of lessons, but I got it in 7 minutes on Khan Academy (in a way that I can actually understand). Man, I love Khan Academy. It's the only reason I'm passing my calculus class.
@AD-wg8ik3 ай бұрын
was it worth it
@mrslovvet10 жыл бұрын
Not that it really matters, but in the yellow line at the top where you expanded the series, the third term has a 4 in the denominator when it should have a 3 (n = 3). Otherwise, awesome video! These really help me study for my midterm.
@jasonvegan576110 жыл бұрын
Yea, the series wasn't expanded correctly but I think most people probably noticed the error so no big deal
@raycooper19438 жыл бұрын
+Jason Owen Yes, it was noticed, and it is not a big deal.
@sudiptoghosh57406 жыл бұрын
Yes it is quite conspicuous
@frettchen14983 жыл бұрын
Thanks! I was really confused at first
@sathvikswaminathan79334 жыл бұрын
the values x=4 and x=-4 also need to be checked since at those values, the ratio test in inconclusive but by the p series and alternating series test, it can be proved that at these two values, the series converges. Therefore x belongs to [-4,4] and not (-4,4)
@masonbanas98645 жыл бұрын
Khan Academy, I can't thank you enough for making something so hard to understand in class so easy to understand from you. What you do is beyond appreciated, please never stop doing what you do my guy.
@manuelhernandaz21476 жыл бұрын
I just want to say thank you for doing these comprehensive videos. My calculous teacher just can’t seem to explain it so it clicks, your really helping me save my grade and learn. Thank you
@thedarkgenious79675 жыл бұрын
thanks. My calc 2 professor went on for 4 hours of drawn out rambling over 2 lectures trying to teach us what the radius of convergence/interval of convergence was and how to find them. I learned more in this 7 minute video than those lectures.
@chesterfieldtales13403 жыл бұрын
Same.
@magicguy19889 жыл бұрын
Technically you need to check x=4 and x= -4 for convergence since the ratio test yields no conclusion when L=1
@yongbowang14447 жыл бұрын
Agree
@paulyu77396 жыл бұрын
Exactly
@nolanison66426 жыл бұрын
You plug those points in for x and solve that particular series for convergence.
@Grassmpl5 жыл бұрын
Yep that's right. In this case both endpoints converge by the p-series test
@zsolttildy57427 жыл бұрын
tryna do the question and the same time as sal and lowkey beat him then he starts pulling out the copy paste function and you know its game over smh sal
@cortisol_induced_coma2 жыл бұрын
I wish all professors could explain things as simply as you
@krazywyatt26386 жыл бұрын
Thanks man, you're a great teacher!
@kazlee6909 Жыл бұрын
Thanks Ryan Maccombs!! Good video as always :)
@sandeepchoudhary40655 жыл бұрын
you my friend are a life saver Thank you so much.
@Copybook2 жыл бұрын
I can't imagine life without Khan Academy
@edrinabenes97548 жыл бұрын
when n=3, isn't the second term of the denominator 3^4?
@windowslogo35775 жыл бұрын
it is.
@ansarsultan3 жыл бұрын
thank u very very very very much
@hurrdurr258 жыл бұрын
but you didn't check the endpoints
@epicgamermoments49004 жыл бұрын
As far as I'm aware, the endpoints don't affect the radius of convergence. The radius is the same whether defined as (a-R, a+R) or [a-R, a+R]
@priyanshmehta99884 жыл бұрын
@@epicgamermoments4900 Yeah, it doesn't affect the radius of convergence, but he has to check that for interval of convergence
@shreeramaashokaadakoli67844 жыл бұрын
You're awesome sir Sal thanks a lot
@mazahiranjum1756 жыл бұрын
Thanks a lot Khan academy
@luciazazel26833 жыл бұрын
Thank you for doing what you do!
@stumbling8 жыл бұрын
Is it accurate to state?: "For arithmetic series, the *difference* between consecutive terms is constant. For geometric series, the *ratio* between consecutive terms is constant."
@monicaelizabeth40698 жыл бұрын
Yes
@Grassmpl5 жыл бұрын
BOTH of what you boxed were the interval of convergence. The radius of convergence is the number 4 itself. Half the interval length
@nosirrahonline2 жыл бұрын
Thank you
@cookiesizYumaah5 жыл бұрын
Thank you! Great work!
@aiicwyt67687 жыл бұрын
Shoutout to Mr. Achille’s class!
@ZephyrCheez3 жыл бұрын
You made a mistake in the beginning, the third one should have 4^3 * 3^4, since n is equal to 3 in that scenario
@mahimakalani26472 жыл бұрын
Thank you is all I wish to say...
@bowenjudd10286 ай бұрын
I'm in foundations and we defined R = 1/lim sup |c|^1/k
@cristianferretty69718 жыл бұрын
thank you so much man, seriously.
@alexwhetstone4464 Жыл бұрын
thankyou
@ivideos73483 жыл бұрын
Thanks !
@echessbee6 жыл бұрын
Brilliant!
@Vathanaization7 жыл бұрын
Thank you so much
@jackzheng85352 жыл бұрын
you are king
@m.sripadh43385 жыл бұрын
will you please tell me the software name which you are using?
@zhangdingkang7819 жыл бұрын
Thank you!
@freyappari6 ай бұрын
W explanation
@nishasingh-yu6ln7 жыл бұрын
but sir what about at point x =4 and x=-4 ...we have to check at end points.....
@harrisonbellis81786 жыл бұрын
I haven't had lectures on this yet but intuitively I guess you should put x=4 into the expression for the general term of the summation to get a P-series which in this case gives 4/n^4 or 4 times the sum of 1/n^4 which is a convergent P series.
@candykiss0246 жыл бұрын
Yeah, all you do is plug it back in and use some tests to see if it converges or not
@mechwise681112 сағат бұрын
The radius is 2, because it is always half of the interval
@froh_do44313 жыл бұрын
how we are going to know that something has to be < 1 for convergence at 6:00? Is that a more complicated statement to show at this moment?
@tylerdee75293 жыл бұрын
The Ratio test says that as long as the limit to infinity of the ratio is less than 1, it converges. After simplifying the limit of the ratio, we are left with an x-term. So basically the function converges if this x-term is less than 1
@michaelfjmusic6 жыл бұрын
Extremely helpful video, but I don't understand why he was able to simplify (n + 1)^4 so easily? It just seems too good to be true and I don't fully understand it.
@annie_adler5 жыл бұрын
Michael Judd actually, you don't need to expand it in full. As the video shows, the only thing you need to know about (n-1)^4 is that its term with the highest order is n^4. That's enough for you to simplify the limits.
@real_john_doe6 жыл бұрын
The fact that he missed n=3 in the denominator in the very beginning makes absolutely no difference here. Stop nitpicking.
@babingurung2558 жыл бұрын
Beautiful
@curtpiazza1688 Жыл бұрын
Great ! 😊
@whoisbobby38 жыл бұрын
N=3 is wrong
@musahamza58298 жыл бұрын
Thanks a lot. . .
@titusadams528810 жыл бұрын
thank you!!
@RCstrava2 ай бұрын
Yay finally get it
@MrBoriskaful7 жыл бұрын
HOW CAN I KNOW WHICH TEST I SHOULD APPLY WHEN I SEE THE QUESTION I AM GOING CRAZY AHHHH
@nihalgupta50097 жыл бұрын
sir,which software is this?
@drmichaelsunsschoolformath2 жыл бұрын
At the start when you say x=1,2,3.. u mean n=1,2,3...
@jacklazzaro98203 жыл бұрын
0:59 That’s wrong. It’s 4^3 * 3^4.
@plasma83213 жыл бұрын
what if its, the ones that gives you more than one number?
@HowViolet2 жыл бұрын
I never listen to lectures anymore... and my grades couldn't be better.... is that bad lol?!
@1Naif7 жыл бұрын
Awesome
@BROBOTwithhope8 жыл бұрын
wrong im pretty sure, or he made an error in the middle and fixed it later somehow