Convergence of a geometric series (KristaKingMath)
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- เผยแพร่เมื่อ 22 มิ.ย. 2024
- ► My Sequences & Series course: www.kristakingmath.com/sequen...
Learn how to determine whether a geometric series converges or diverges and if it converges, how to find its sum.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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No wasted words. No skipped steps. She knows exactly what she is going to say throughout. Complete command of the material. Precise, organized, clear. Each tutorial is like a music recital.
Thank you very much!
You've got it great sea. She's the best math teacher on youtube. I spent a couple weeks shopping around on TH-cam and am so glad I found.
Exactly my thoughts, she is a mathematician to the core and a teacher by profession : D
Thank you for taking the time to comment! I really appreciate it. :)
Deserves more views.
This girl has taught me more about series in 11 minutes that a 20 year professor has in half a semester, seriously thank you so much!
+jacob long I'm so glad I could help! Thanks for the comment Jacob!
I have never commented on a video, but you Krista are the BEST I mean absolute best teacher I have yet seen. Thank you so much for your videos.
Awww, thanks Mehak! I'm so glad you're enjoying the videos!
thank you so much krista. you make who is the most dummy person in math easy to understand what is geometric series... gosh, thank a lot yhoo
You're welcome, Faten! And I'm sure you're not a dummy! :D But I'm so glad the video helped!
Thank you so much for your video. It is really easy to understand and you explain things step by step which is awesome for people like me who don't understand math so easily. Thank you for being an excellent teacher!
+Priscilla Celeste I'm so glad it made sense!
wow i can actually understand this. You make calc seem so much easier. thank you so much for the videos :)
You're welcome! Glad you like them. :)
Well explained. Thank you so much!
I am not usually commenting on youtube videos, but this time i can't help it....you are really awesome and made it a lot easier to grasp....Thank you so much and keep up the good work...you are the best :)
very well explained, nice to see it converges
thanks my test is at 5:30, now is 3:41. Helps A LOT.
I hope the test went great! :D
Thanks for showing a geometric series that alternates between negative and positive. When not given the summation, and just a first few numbers of the series, I'm always inclined to immediately jump to alternating series. This cleared up a few things for me. Much appreciated.
I'm so glad it helped! :D
Interesting and well explained...Thank you!
Thanks! Glad you liked it! :)
Beautifully done. Thanks for all the help in my calc course!
+Kevin Lin You're welcome, I'm glad I could help!
I always enjoy your tutorial videos..thank you
These videos are wonderful. Thank you!
Awesome! Thanks for letting me know. I'm so glad you like them!
you're my savior! Thanks so much for posting your videos!
I'm so glad they're helping!
This is the best and the easiest tutorial in calculating geometric series.. U should put something different in the title, since it's different method ♥. Like trick or new way or different way etc..
I don't even know why I go to my 6th period calc class when I could just watch your videos. I swear my teacher talks in code sometimes. Thank you so much!
+Elle Chaves You're welcome, I'm happy to help!
BIG THANKS KRISTA!! You really helped me on my Kumon
You're welcome, I'm so glad I could help!
Thanks for this valuable maths course,
Glad you liked it!
Thank you, for a great video in geometric series. very helpful!
You're welcome, Cyrus! I'm so glad you liked it! :D
DAMN. you really helped me for my final! thank you so much for your hard work!!!
Awesome! So glad it could help. 😊
Thanks Krista!!!! :)
+Psychedelix You're welcome! Glad you liked it!
Hey Krista, thanks for all of your videos! I just had a quick question. What do you do if your sum originally starts with n=2, or n=3 etc...?
You would want to try to roll it back to n=1 or n=0, depending on what you need. Try plugging n=1 into the series to see if it still follows the same pattern. :)
Useful upload, and btw your voice is unbelievably beautiful :)
You're the best!!
Awww thank you so much!!
Thank you!
You're welcome! :D
When are you going to do more vector calc? Stokes greens thrm, divergence curl etc etc...?
they're coming this semester! :)
thanks i liked such amazing way u are explaining the lesson ohm thank again for ure post
you're welcome, i'm glad you liked it!!
Thank you and it was useful. However,
I just wonder is why |-3/4|=3/4
Thank you very much ❤️ from india
ive noticed that a lot of the problems that you are going over are from Stewarts Calculus textbook. Is that by any chance the book you are using?
How would you do: sin^n( pi/4 + npi)? Where n=0. Hopefully that makes sense the way I wrote it.
What would be the limit? What does it converge to?
Sorry I'm not catching on right away, but I'm "back in" x-y graphs, and I'm thinking "what is this supposed to look like on a graph?"
But no, sequences aren't "X-Y", they are just a column of numbers. Ok, that said, "divergent" just means "get bigger" (absolute value), and "convergent" just means "get smaller" (absolute value). (right?)
+hettygreene yes. if a series diverges, then the series is continuous. If the series converges, then it reaches a value and cannot continue.
So helpful! I have a final tomorrow night and I missed a class and it was based around geometric series. This saved my life! Haha! Thank you so much!
Good luck tomorrow!
I received an 86 on the final giving me an A for the semester! Thanks again!
Joey Kane Yaaaaay! That's so awesome! Thanks for letting me know. :D
Joey Kane Fuck, this is a B+ in my college, and if you lose two marks more it would be B ☺.
Yeah, I landed an A in that class!
the process on how to find r end at 8:55 . your welcome
Thank you!! :)))
+PuffPuffBunny You're welcome!
Lovely, thanks a lot. I can't figure out these questions in my Mid-Semester Exam... Now I find you, it is a bit late to me :( But you are better than our professor I swear.
You're welcome! I wish it had been earlier, but I'm glad the videos are helping now! :D
Krista King I will watch all your video before my Final Exam :)
thanks now I know how to get r from the series
My question here is why you start with n = 1 instead of n = 0?
At 9:38 : "The sum of a geometric series is always just a/(1-r)"... Only if it's an infinite geometric series, and it converges (|r|
If the given formula doesn't make it obvious, how many terms of a series do we need before we can feel confident that we have a consistent pattern?
You're magnificent! Thanks for the video I hope you'll do couple of examples! 😘😘
Thank you so much, Djamel, I'm so glad you liked it! :D
i don't get the significance of the sum.. is it where it converges to?
Thank you so much for your lecture, i just wonder what would be the formulae for finding the sum of the series
a+ar+ar^2+................+ar^n-1 if r=1
i will be very grateful if you give me reply
thanks
If r=1, then you end up with a+a+a+a+a+a+..., which is a series that doesn't converge.
Means there is not solution?
Right. You can't find the sum because it doesn't converge.
thank you for saving me from a D in pre-calc
Think you
+عبد الكريم عبد الكريم You're welcome!
GIB UP!!!
you never fail to blow my mind... putting all the other online math teachers out of business!
so what is a geometric series?
Nice
Thanks!
how is that possible to find sum of the geo.series its going infinite??
It's only possible when |r| is less than 1
|-3/4| is 3/4 so it converges
If |r| is less than 1 then as you keep adding values the numbers keep getting smaller so the sum approaches a value a/1-r
1 + 1/2 + 1/4 +1/8 + 1/16 + 1/32 + 1/64 +1/128 + ...
S=1/1-1/2 S=2
I fuckin love you. You make everything so simple.
lol :D
Jesus, with 675 videos I thought you'd be done by now! How much of calculus is there?
Intergral Calc is a beast. She doesn't stop. She's out of control, she's solving everything and making our lives easier
Borg status
the best part is Ta ta ta.............
Like it.
Thanks!