Geometric Series - Proof of the Sum of the first n terms : ExamSolutions

[@robertgroves5630]

this was the best geometric series video i have found

[@sumayahkazie1243]

11 years later.... And your video still performs miracles🌸... 11 years ago we were in grade 1.... Good luck to all matrics of 2021.... We can do this🙌🙌🙌❤🌈

[@happytagged3646]

Thank u so much 🥰💖🥰💖

[@mpumimaarman426]

Best of luck for tomorrow ❤️

[@kamabokogonpachiro6797]

now its one year after a levels if u did that?

[@olivegirl_]

It's still so helpful even after 14 years! Good luck everyone in 2024!!

[@ExamSolutions_Maths]

No probs - pleased to hear that it helped.

[@josephgitau280]

Im a maths teacher but all along ive never had better explanation of this to students. Thanks so much, I have gotten it now!

[@CallMeIshmael999]

Thanks for this. I've proven this by induction before, but I never thought to prove it this way. And this video was clear and well-produced.

[@sinthianawar513]

how do you prove it by induction? can you please give me a link that helps

[@aaqilzuhair7161]

Helping us lads even 10 years later. Thank you legend!!

[@SanauKantai]

I'm in uni now and I still use your videos. Thank you

[@ExamSolutions_Maths]

I'm pleased to hear that they are stretching that far and that they are helping you. Hope you get on well at uni.

[@harryemataj666]

Yep same

[@danjones4492]

AWESOME!!! I have been doing A-Level Maths for about 6 months and I think I know pretty much everything on the the course, but I could never remember the proof for the AP and GP questions. Now I understand what they are all about. Cheers Mate

[@danjones4492]

dan jones I am defiantly subscribing. Brilliant!!!!

[@jeremyyeleyko5636]

You've made it look so easy! Thank you so much :)

[@Leonitusworm]

Do you know how I could prove the series is bounded from n=1 to infinity? where we have p^k as our sequence and 0

[@eyesontheprize19]

Lovely video Very helpful, thanks❤

[@lindelwamnisi1561]

22 January 2022,11 years later!this video is still very much relevant and easy to understand.thank you very much!

[@notimportantok]

This is most helpful!!! I am glad there is someone that can explain this better than my teacher!! you Have saved my c2 maths paper of disaster !! Thank yOu

[@banumathidandapani2782]

Best teaching and clearly explained

[@jacobhouston1655]

1:55 The only person in the Internet that explained the R to the N -1.

[@benwatkins10xd]

nice video mate, paper 1 tomorrow lets do this

[@thevaultdwellerf6691]

I'm shitting bricks for tomorrow aha

[@benwatkins10xd]

update : that paper was absolute toss

[@freezy2755]

@@benwatkins10xd did you do good

[@benwatkins10xd]

@@freezy2755 yeah i graduated with a first in bsc physics cheers lad

[@Gitredmon]

Thank you so much!! Got C2 tomorrow and only realised tonight that I didn't know this! Saved my arse!

[@niravdave5813]

allie

[@madz2425]

Matthew Clarke-Williams lol 3 years down the line and I'm n the exact same position as you XD (I have C2 tomorrow)

[@suran3743]

Same here! Good luck

[@calebd2513]

Same here, good luck :)

[@johnnybain216]

good luck boiz

[@JaacobRS]

Great that you do these videos, thank you.

[@ExamSolutions_Maths]

JaacobRS Thanks for using them and I hope they continue to offer you support when needed.

[@sadiyosharaf1318]

thank you so much you helped me

[@ufewlufewlx605]

Very nicely explained sir, particularly like the last instruction to remember the method, I kind of vaguely just remembered the formula. However remembering the method is best. So "multiply by r, and take it away, factorise out Sn then divide by 1-r". Hoverer, if you just remember "multiply by r and take it away" you can with a bit of though get the solution I hope.

[@xujiechen626]

i was confused for 20 mins tysm!!!!!

[@irish9962]

good skill of teaching thanks for this video

[@JacobFoxChannel]

That was fantastic you wonderful man!

[@Eoghan0C]

Great video, nice and simple, thank you!

[@ExamSolutions_Maths]

@Vupadhayay So that we can eliminate many of the the terms. It's a clever technique.

[@vartonic7812]

this video actually saved me. thank you very much!

[@Refined_Notion]

Very clear and informative. As always, thanks for the upload.

[@ExamSolutions_Maths]

Pleased to hear that it now makes sense.

[@thebush6379]

I'm glad to know where this formula came from. Even though if I try to see how the formula itself makes sense is still confusing

[@Kira56856]

Thankyou sir

[@ufewlufewlx605]

perhaps worth noting you can do the subtraction either way and the middle terms still disappear. Hence you will have (r-1) terms rather than (1-r) you will also have (r^n - 1) and (1- r^n)

[@ExamSolutions_Maths]

Yes. Good question. Note that the formula is only true for r not equal to 1

[@Fibra73]

I am curious as to how you know to do what you did in the proof? Where does that r multiplier and the subtraction come from? Was the sum created first by noticing the pattern? Or was the sum proven first and turned into the law?

[@DelltaAce]

Thank you! Resitting a resit tomorrow and finally get this! Going in confident now! :D

[@timgill7117]

Thank you so much

[@tomasbeltran04050]

just what I've been looking for. I've seen it often, but always forgot it

[@DGR270]

Thanks. This has made my A-level past paper a lot easier

[@hounamao7140]

my god I've been looking for something like that for an hour and a half, thank you

[@ExamSolutions_Maths]

Thanks for watching

[@maher4art951]

Thank you sooo much even after 11 years

[@jojo-dr8tp]

Thank you sir....

[@BigBangGDbabyyy]

hi there, this was a really good explanation, but I don't understand the purpose, other than to cancel out factors, or subtracting equation 2 from equation 1? thanks

[@Vupadhayay]

Thanxz alot the video give very nice and simple explanation. I have 1 simple question may be it sound senseless but i have been always wondering WHY WE NEED TO MULTIPLY OUR SERIES WITH r to get the another series and WHY WE ARE SUBTRACTING Sn with rSn???

[@KurdishFalconPKK]

Thank you for this video. It really helped to clear things up for me regarding this proof.

[@sankar7446]

Thanks it helped me a lot.

[@ExamSolutions_Maths]

Good to hear. Best wishes.

[@shining_solana789]

Is this only applicable if r < 1?

[@untilm]

Thanks. Teachers just give us the formula and don't explain them, so I have to watch videos like this to fully understand what I am learning.

[@noonecares6816]

could i ask what is the purpose of multiplying r by rSn

[@sadmanzaid420]

In order to generalise the equation so that it applies to any geometric sequence, if you do the proof using numbers you'll understand that it provides an incredibly fast and efficient method of calculating the sum of any geometric series.

[@Romans10.17]

THANK YOU SO MUCH!!! You are such a great teacher and explain things in a way that just make so much sense.

[@ExamSolutions_Maths]

Very kind, thanks. I wish you every success and thanks for your support.

[@ExamSolutions_Maths]

Cool. Should get full marks then I hope.

[@Harry-Phatmamba]

I have C2 on Friday this is really boosting my knowledge.

[@BigBangGDbabyyy]

sorry i spelled it wrong - i dont understand the purpose of subtracting the equation 2 form equation 1? thanks

[@babymonkey1993]

THANK YOU THANK YOU! so much. You just saved me from an F on my exam, which is tomorrow.

[@ExamSolutions_Maths]

@SaronArul Good to hear - thanks

[@MagnusTheUltramarine]

What's the reason for multiplying Sn by r?

[@williamparrish2436]

You are one of the few people that actually seem interested in UNDERSTANDING what is happening, instead of just nodding your head and going along with the flow. Thank you, that is the same question any reasonable person would ask.

[@LegendaryHeroponRiki]

i dont understand how this works all videos just show what to do and not explain it thoroughly ​@@williamparrish2436

[@TinHinge]

Oh my am I glad I looked at this yesterday :P It came up in the paper I was sooo happy! Thank you so much :P

[@randomguy2554]

this is beautiful !! , thanks !

[@voldy3565]

I need to find the sum if the first 10 terms, I have given a1+a5=51 and a2+a6=102. How do I do this?

[@chachachi-hh1ks]

Thank you for keeping this video👍

[@natdaman5]

thank you so much, really clear and helped me with my homework!

[@williamparrish2436]

Can someone explain WHY we multiply by r? Or is that something ELSE I should already know before I know it when doing math?

[@ExamSolutions_Maths]

It is now. Thanks

[@iamgroot2810]

Very helpful video. Great job!

[@moazzamkhan507]

when are we going to see exam solutions' face. i need to put a face to this incredible man!!!

[@perfectnails_diy]

This video really helps! If it helped you too then like and subscribe

[@JulianGonzalez-ej2fi]

What compelled you to subtract equation 1 and 2?

[@jvillalobos6988]

well, this is one of the cases, but what if -1

[@zoeredadams]

villa woolf if r is 1, then the series wouldn't increase by anything! 1^1 is the same as 1^100, so the sum of the series is just a*n. But yes, you'd make that assumption.

[@malanhemal6574]

sir, what is the reason you mulply by r?

[@donnakebab990]

Thanks for explaining so well , your the boss man.

[@InquisidorOmega]

Absolutely fascinating

[@toviewandcomment]

very helpful and clear, thank you so much.

[@Kilda61]

Thanks, great video and great explanation!

[@ExamSolutions_Maths]

You are welcome

[@SexyFatGuyoo]

thank you so much for making these videos you helped me alot!

[@HVS2328]

Why Sn equation ends with power n-1, even knowing the last no. will end with power n?

[@musawwirahmad6396]

Thanks, helped a lot

[@BigBangGDbabyyy]

also, how did you get ar^n-1 from ar^n-2?

[@MrDream996]

WHY do you time Sn by r ?? Where does that come from??

[@vino2476]

You brilliant soul, Thank you

[@ExamSolutions_Maths]

Just multiply top and bottom of the fraction by -1.

[@solaawosika2986]

It why must we do equation 1-2

[@ExamSolutions_Maths]

It eliminates most of the terms and allows us to develop Sn

[@javishkarrosspooran6399]

Thanks dude. Helped a lot...

[@aliceJLinwonderland]

thanks very clear explanation

[@Gunny369]

Sir, Thank you soo much on doing this video! I was so confused looking at this formula in my Calc textbook!

[@ExamSolutions_Maths]

@DelltaAce I hope it comes up now for you. Good luck.

[@WarKoreanZombie]

Link in the description isn't working.

[@masnoonhasin2714]

Thanks from Bangladesh.

[@mechvex8726]

You made a mistake i think the ar^n is suppose to cancel out all we are going to be left with is a because if the series continues we will get to ar^n and that will cancel

[@ExamSolutions_Maths]

Are you talking about the proof section? Actually ar^n would not cancel out since there is only one ar^n in the series and that is at the end. so the first equation - second equation would be a-ar^n

[@mechvex8726]

@@ExamSolutions_Maths so the series is finite

[@mechvex8726]

@@ExamSolutions_Maths I’m saying if it kept going thru would all cancel right ?

[@mechvex8726]

@@ExamSolutions_Maths I agree with you if the series ends there but if there both infinite you would just be left with a

[@m.ismail1069]

Thanks

[@ExamSolutions_Maths]

That's fine - pleased it helped.

[@WhiteChrist83]

very good explanation

[@08jmb2010]

Thanks :) Great Explanation

[@ExamSolutions_Maths]

Good luck for tomorrow.

[@BillyNguyen95]

Normally i do C2 well but not for the Exam this year . . I think C2 exam this year is not too hard but It make us have to think a lot to solve the Question . I found that i also get in trouble in Tan and Cos sign question too. Some of my friends done in only 45 minutes . OMG ! Im a little bit scare the C2 Exam this year . BTW , Both of we get the pass results.

[@sonumaity3404]

Nice explanation

[@RichardSng94]

Thank you so much!!! Now I can finally sleep well at night haha

[@ExamSolutions_Maths]

I can now sleep well knowing your sleeping well.

[@94D33M]

I spent half an hour bruteforcing to derive this sum.... Eventually I ended up very close except the bottom term instead of r i put n because i was just using small numbers for initial testing. Though I don't like how everywhere I see 1 Infront of the r. I like to write it as S = a(r^1-1) \ r-1

[@Seat1A]

ExamSolutions, your amazing.

[@sajnivarsani5277]

Made my day this

[@bingzhewho]

sometimes i wonder how do people find those genius solutions

[@ExamSolutions_Maths]

@owix2 Just multiply top and bottom by -1

[@Tmnt2407]

Thanks alot!