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.

[@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

[@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

[@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!

[@aaqilzuhair7161]

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

[@jeremyyeleyko5636]

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

[@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!!!!

[@xujiechen626]

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

[@eyesontheprize19]

Lovely video Very helpful, thanks❤

[@banumathidandapani2782]

Best teaching and clearly explained

[@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

[@sadiyosharaf1318]

thank you so much you helped me

[@lindelwamnisi1561]

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

[@irish9962]

good skill of teaching thanks for this video

[@jacobhouston1655]

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

[@ExamSolutions_Maths]

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

[@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

[@Eoghan0C]

Great video, nice and simple, thank you!

[@JacobFoxChannel]

That was fantastic you wonderful man!

[@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

[@SagnikDatta-g4o]

it was like straight to the point. understood super easily. THANK YOU

[@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.

[@ExamSolutions_Maths]

Pleased to hear that it now makes sense.

[@Kira56856]

Thankyou sir

[@vartonic7812]

this video actually saved me. thank you very much!

[@DGR270]

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

[@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.

[@hounamao7140]

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

[@ExamSolutions_Maths]

Thanks for watching

[@sankar7446]

Thanks it helped me a lot.

[@ExamSolutions_Maths]

Good to hear. Best wishes.

[@DelltaAce]

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

[@jojo-dr8tp]

Thank you sir....

[@maher4art951]

Thank you sooo much even after 11 years

[@Refined_Notion]

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

[@tomasbeltran04050]

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

[@ExamSolutions_Maths]

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

[@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]

@SaronArul Good to hear - thanks

[@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

[@randomguy2554]

this is beautiful !! , thanks !

[@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

[@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

[@chachachi-hh1ks]

Thank you for keeping this video👍

[@babymonkey1993]

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

[@natdaman5]

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

[@ExamSolutions_Maths]

Cool. Should get full marks then I hope.

[@KurdishFalconPKK]

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

[@iamgroot2810]

Very helpful video. Great job!

[@donnakebab990]

Thanks for explaining so well , your the boss man.

[@SexyFatGuyoo]

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

[@toviewandcomment]

very helpful and clear, thank you so much.

[@ExamSolutions_Maths]

It is now. Thanks

[@Harry-Phatmamba]

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

[@Kilda61]

Thanks, great video and great explanation!

[@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]

@KSaiyu That's ok

[@musawwirahmad6396]

Thanks, helped a lot

[@InquisidorOmega]

Absolutely fascinating

[@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.

[@javishkarrosspooran6399]

Thanks dude. Helped a lot...

[@ExamSolutions_Maths]

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

[@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???

[@Sneha-wt6yk]

Wow thanks a lot❤

[@Gunny369]

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

[@vino2476]

You brilliant soul, Thank you

[@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.

[@08jmb2010]

Thanks :) Great Explanation

[@perfectnails_diy]

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

[@aliceJLinwonderland]

thanks very clear explanation

[@masnoonhasin2714]

Thanks from Bangladesh.

[@TheBoatThatrocks94]

i love you , great explanation

[@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

[@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.

[@Tmnt2407]

Thanks alot!

[@moazzamkhan507]

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

[@WhiteChrist83]

very good explanation

[@ExamSolutions_Maths]

You are welcome

[@Mmovies72]

thanks mate great viedos

[@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.

[@m.ismail1069]

Thanks

[@ExamSolutions_Maths]

That's fine - pleased it helped.

[@AJ-et3vf]

Great video! Thank you!

[@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

[@sonumaity3404]

Nice explanation

[@sajnivarsani5277]

Made my day this

[@BigBangGDbabyyy]

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

[@ExamSolutions_Maths]

@gautamv8 Thanks

[@fawadkhan4548]

thanx you made it simple

[@ExamSolutions_Maths]

🙂

[@ExamSolutions_Maths]

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

[@Seat1A]

ExamSolutions, your amazing.

[@ExamSolutions_Maths]

@owix2 Just multiply top and bottom by -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?

[@kamraman123]

thank you!

[@ufewlufewlx605]

Someone asked why multiply by r? That is a good question because it helps you to remember the whole thing. When you multiply by r and take it away all the middle terms disappear. So if you just remember "multiply by r" those 3 words can give you the solution!! Simples!!

[@shining_solana789]

Is this only applicable if r < 1?

[@ExamSolutions_Maths]

@stripesfreak Hope it does for your sake - Best wishes

[@AyeOldSponge]

THANKS SIR!!!!!!!!!!!!!!

[@miceguy]

This explains so much better than Wiki lol.

[@hninhninthawyuoe2962]

u make me better

[@ExamSolutions_Maths]

Good luck for tomorrow.