Convergence and sum of a geometric series, example 1 (KristaKingMath)

[@Glacierai]

Clear, no fancy jargon, and a useful "how" instead of "why" explanation. Absolutely excellent.

[@FubarGame]

I find it awesome that you take the time to respond to many of these comments. Thanks again for the videos.

[@kristakingmath]

@fingerboy18 Absolutely! Thanks for watching!! :)

[@u0432865]

Thank you so much. It took a PhD student like a week to try to teach me this. You're the best.

[@kristakingmath]

@St1florida That's awesome to hear! Sort of. :) I'm sorry about the CALC class, but glad you found what you needed in this video! Thanks for your support!! :)

[@SilverTheRain]

I cant personally thank you enough for making calculus II so comprehendible. it is a real shame that i didn't find your videos before flunking the corse. however, watching your videos I know that I can get a better grade next time round. cheers.

[@squirealan]

you actually make sense! ive had such anxiety over my cal 2 but watching this it was like oh!.

[@junaididris3797]

I so much love you and your strategic teaching method You're inspiring

[@mkraft1212]

very thorough and well done! thanks so much, the infinite series chapter has been tough

[@kristakingmath]

you're welcome!! i LOVE it when people comment, so i always try to respond to them!! :D

[@nniibblleess]

YOU ARE AWESOME!!! Thank you for these fantastic, easy-to-understand videos!

[@kristakingmath]

Aw thanks! I'm so glad you like them. 😊

[@kristakingmath]

@starofcctv94 I agree. I'm trying to teach the method, not really the particular problem. :)

[@kristakingmath]

@jayspenh Only because I haven't had a chance to do videos about them yet. I'm adding content as fast as I can all over CALC I and II topics. Hopefully I can get Harmonic Series uploaded sooner rather than later! :D

[@kristakingmath]

I hope it helped!! :D

[@mohanmustafa]

Very thankful to you for posting this video

[@kristakingmath]

@MrWonderfullable I love that feeling when things start to click. :) Glad I could help!

[@kristakingmath]

You're welcome!

[@kristakingmath]

I'm so glad you liked it!! :D

[@MrAmansyed]

thank u so much.:-) This was two days before my exam and i went to bed but i couldn coz i was worried....but thanks to you i learnt something while relaxing:-)

[@kristakingmath]

@squirealan That's soooo awesome! I know how much it sucks to sit through class when you're not getting it, and how good it feels when it CLICKS. :) Thanks for letting me know, because it makes me so happy!! :)

[@kristakingmath]

Thanks!

[@kristakingmath]

ha...that may be too much stress. :) Glad you like the videos!

[@kristakingmath]

@MrAmansyed I'm so glad! :D

[@kristakingmath]

Stay confident and keep practicing and you'll definitely do better next time around. :)

[@CALI714GS]

good solid explanation! Thanks

[@kristakingmath]

Thanks!

[@RandyLott]

Very good video. Thank you for sharing.

[@kristakingmath]

awwww thanks! you're very welcome, i'm glad it's helping! :)

[@kristakingmath]

You're so welcome! :)

[@kristakingmath]

@saqar8888 You're welcome!! :)

[@kristakingmath]

You're welcome! :)

[@jayspenh]

How come you do not have Harmonic Series on your website?

[@tommytoks3675]

i really love this video

[@St1florida]

Thanks so much. I got in 14 minutes what i couldnt get in a 2hour calc class.

[@InfinityLord5]

Wow... I understood 99% of that! You make it so easy and I am only 12!!

[@meganjoy1693]

Someone answer this quick!! Is r positive or negative? Bc i thought it was |r|

[@kristakingmath]

r can be negative, but when you plug it into |r|

[@MegaBdboy]

Do you have any videos with sequences of functions ?

[@NarrowEdgeTrading]

Are you a math major? Or have you just taken higher level math courses required for engineering/computer sciences?

[@degio123]

thanks alot! now i feel alot better for my upcoming exam =)

[@Süleymantürkçe]

thanks alooooot ! i never expected to understand what's going on with series :S !!

[@kristakingmath]

you're welcome!! :D

[@samanbandana]

good video, thanks for sharing.

[@AlvaroZamora]

The longer method shows more of the fundamentals of infinite series, though. What you did here was simple algebra.

[@coilstapped]

Great video, how much math have you had?

[@SafeAndEffectiveTheySaid]

I'm so in love!

[@vinaynayak1993]

This is an amazing video. I feel much more relieved after I watch your videos on Calculus topics! You should teach at Penn State University haha :)

[@stan021]

it very very good explanation...

[@kristakingmath]

only two intro calc classes. the rest i've taught myself. :)

[@Soc23Box]

Why are you using 1/(1-x) for the sum formula instead of a/(1-x)? is there a difference?

[@kristakingmath]

+Soc23Box That "a" just represents a coefficient out in front of the series. If there isn't a coefficient, then really the coefficient is actually 1, so the formula turns into 1/(1-x). You could also think of the formula as a[1/(1-x)]. So really it's just the 1/(1-x) that gives you the sum of the series, and you've just got to remember to multiply by "a", whether "a" is 1, or any other number. I hope that makes sense!

[@kristakingmath]

@bcjn16 Neither! I just love calculus! .....sorry about that earlier, wrong account :)

[@SebastienPatriote]

Actually the final answer should be 7/33, as it is customary to use the most simple fraction possible. Wow, that is a complex way of just dividing your recuring number by 99, since 21 has two digits, if it were .456 recuring (three digits in 456), your fraction would be 456/999 or 152/333.

[@kristakingmath]

12?! That's impressive!

[@MeistroJB]

Ever get a professor that knows what the problem is? Not that often, huh. What do they care? But here I'm trying to anticipate the answer and of course I forgot the 21/100. and got L=1.010101.... wrooong.... So guess what Prof. Krista points out as soon as I click 'resume' -> yep, you guessed ut.... the 21/100 ('! deleted - nothing factorial here... heh heh..). Try not to forget the coefficient - just because it pops out of the summation... She not only knows how to solve the problem, she knows what the problem (for the rest of us...) iS! Professor Krista's the best!

[@cliffordwilliams473]

Where can I find an example of something like finding the sum from 0 to infinity of (2^k)/k!

[@kristakingmath]

Clifford Williams Similar: kzbin.info/www/bejne/q36vc3RseK2FZ6c

[@SevenRiderAirForce]

=7/33 Good job! Excellent walk-through.

[@kristakingmath]

i'm glad!! :D

[@kristakingmath]

@MrSaad1932 Indeed! :)

[@Anonymous-rt7gh]

Mam your teaching style is very good. Can you please give some lecture of statics and dynamics. I am belong to India.

[@apdelhamedelpasha6213]

good job

[@MrSaad1932]

math is wonderful

[@Yash2634432]

(x-1)(x^2-2).......(x^49-49) what is the coefficient of x^1223 ?

[@kristakingmath]

Only for geometric series. :)

[@OmarRawandi]

a nice explanation ... and a nice shirt too

[@kristakingmath]

@degio123 I'm so glad! And GOOD LUCK!! :)

[@MellowCruisin]

I won't forget to not forget the constant out front ever.

[@kristakingmath]

sounds good...automatic "A" for you. :)

[@saqar8888]

you are amazing thanks alot

[@kristakingmath]

@pigpigpigwwf You're welcome!! :)

[@kristakingmath]

you can find me here :) facebook . com/integralcalc

[@kristakingmath]

@cryora YAYYYYY!!!! :D

[@MrMoeqt]

THANKS ALOT!!!!!!

[@starofcctv94]

that seemed a very long method to find the fraction of a repeating decimal. an easier way would be; let 0.21212121....=x 100x=21.212121.... 100x-x=99x=21 therefore x=12/99 much easier

[@quinlanmoore309]

Subscribed!

[@kristakingmath]

Thank you so much!

[@MrMoeqt]

thats gcse level, its easy. this gives you more intuition.

[@internationalklins]

nice

[@kkkkkkkkkk955]

this is awesome! Please be my professor!

[@saqar8888]

good

[@jayspenh]

@TheIntegralCALC okay great thanks whenever you can =]

[@avengedzeppelin333]

Or you could just do this x=.212121.... 100x=21.2121.... (100x-x)=99x=(21.2121..-.2121...)=21 So 99x=21 x=21/99

[@hodifaabushakra8334]

very very \ thaks

[@Khristian3500]

but 12/99 = 0.12121212....

[@kristakingmath]

@u0432865 Aww thanks!! I'm so glad it helped!! :D

[@samiassmar4814]

i love tou

[@Rayquesto]

yeah this is the convention. i like it better.

[@jimbow6130]

I'm a physics major and I feel like I should be paying you my tuition money...

[@kristakingmath]

That works :)

[@MrJupiter2]

I like looking at your arms jiggle when your writing.nice!

[@MiracleOO7]

Intelligence - check attractiveness - check are you seeing anyone?

[@CookieMonstersUnited]

@starofcctv94 x=21/99 :P but ur points still stands

[@rbliss111]

21/99=7/33

[@kristakingmath]

LOL! :)

[@MrJupiter2]

Good video,nice arms too.

[@kristakingmath]

:)

[@graysongrzybowski943]

u made it kind of difficult on yourself..... why didn't you just write it at 1/10^2, 1/10^4 , blah, blah , blah

[@danielreyesalarcon1891]

I respect your work but I noticed some of your math language wasn't very clear.

[@satishsharma3149]

.

[@datbrayciss]

>implying this shit takes any intelligence

[@snowy0110]

lvoehewshit

[@amartinmeus]

zomg, do you have a boyfriend? (or girlfriend, that's cool too)

[@RolloutCal]

I have a crush on you lol marry me!!!

[@saqar8888]

you are amazing thanks alot