Proof by Induction : Sum of series ∑r² | ExamSolutions

[@Sarank1107]

10 years later and this goat is still carrying further maths

[@thomaslee7507]

You sir are a genius! This video is flawless and helped me grasp the concept in one go! Thanks a lot!

[@ExamSolutions_Maths]

Pleased to hear it helped.

[@cooldude22032]

Thank you, you did a much better explanation than my teacher who thought it would be a good idea to rush through the last chapter of FP1

[@jamescopland2649]

+Matthew Lunn Same here bro we took ages on matrices and complex numbers so ended up rushing the last two chapters; and the exam is tomorrow :(

[@nagul3165]

7 years later, and my exam is 2 days away, I hope y'all are having a good life ✌✌@@jamescopland2649

[@justinemacarat6992]

thats a very straight line.

[@dhvsheabdh]

I assume you're wondering how the hell he's changed the "(k+1)^2" into 6(k+1)? Well: Already, from the equation we can see that there are essentialy two things being added together. We have the Sum from r=1 to k of r^2, equal to k/6(k+1)(2k+1) and (k+1)^2. The thing is, we want to add both of these things toegther. If I make it more simple, it's like trying to add a/6 and b in one bracket without any fractions. It is neccessary to know that b is equal to 6b/6. So (see next comment...)

[@iamkaja0]

OH MY GOD THANK YOU. Exam tomorrow - why didn't I discover this earlier!? Better late than never though, thank you so much!

[@BillStrait]

I'm taking a discrete math course online. This exact problem is on this week's assignment. For the first time since the course began, I feel I understand what's happening. Thanks a lot.

[@AaaAaa-yb2nb]

A huge help. Thanks for the clear explanation. FINALLY understand each step.

[@julesofharbledown9591]

Immensely helpful, thank you. I was missing a step the textbook just didn't explain well.

[@mrboyban]

If you hate proof by induction put your thumbs up

[@dhvsheabdh]

well, the lone k dissappearance is simple. In the equation you can see that (1/6)k(k+1)(2k+1). They are all to be multiplied together, so it makes no difference in which order they are. So abcd = dabc = dcba etc. So he's moved the k infront of the (2k+1), so it makes it seem more simple as he multiplies everything by (1/6)(k+1). So, as (1/6)(k+1) is a factor of (1/6)(k+1)k(2k+1) and (1/6)[6(k+1)^2)], they can be added together, and hence simplified. Message me if you have any problems :)

[@Soojene]

The exam solutions guy is an absolute lad!

[@dhvsheabdh]

So...(k+1)^2 is equal to 6 lots of this, divided by 6. But BECAUSE it has been divided by 6, just like the (1/6)n(n+1)(2n+1), they can now be added together for simplification. However, another common factor in both of these terms to be added is (k+1), so he's decided to take that out also. So if you take out a sixth and (k+1) out of both of the things to be added, you end up with (1/6)(k+1) as the thing outside of the brackets. However, you're probably also wondering where the lone k has gone..

[@GabbersLJ]

Oh my word that was so helpful thank man I was lost as he'll and you have shown me the light, thx so much.

[@ExamSolutions_Maths]

+TheGminister That's good

[@ExamSolutions_Maths]

Check out my website. It is on there.

[@liamchandler8860]

Very clear, thank you

[@ExamSolutions_Maths]

+liam chandler Thank you

[@nuse420]

I do not see where you get 1/6th from both sides the addition sign.

[@ExamSolutions_Maths]

I would have thought so.

[@thatomofolo452]

Will there be a formula sheet 😮

[@ForberEnoch-r3r]

Teaching and learning here is good

[@leoniduvarov6565]

This seems to be a very hard concept for people to explain. I applaud you for doing a great job at explaining it clearly

[@jusyungb4860]

In a paper I first found out wat I was working to towards then realised I couldn’t factorise it towards it, not sure why. But then I worked from rhs to lhs such as expanding the rhs to show it equals to my lhs. Will I still get the Marks cus it’s proved ?

[@ExamSolutions_Maths]

Good luck

[@nini9285]

Thank you Now i really understand the topic

[@aberedenisiokou2929]

Great one sir

[@pragyakansal9017]

this helped so much!!

[@dhvsheabdh]

Can you do more of these Proof by Mathematical induction videos?

[@Fungias]

THANKYOU

[@rosin40]

Great explanation! This was really easy to follow and understand.

[@MEETPANCHOLI07]

hey.....what about 7+10+13+16+....+(3n+4)=n/2(3n+11).....what would the k+1 be?

[@thabanindlovu7367]

I really appreciate your teaching Sir, l'm a step ahead. Thank you.

[@ExamSolutions_Maths]

I appreciate your comment, thank you.

[@ese7560]

Thank you This helps alot🥰

[@ExamSolutions_Maths]

No, FP1

[@linping6905]

Thank you I appreciate thos

[@cary_domiii]

I've been struggling with this problem to find our that my only mistake was that I forgot to square (k+1)....

[@firstname4337]

this was helpful

[@morganabbotts]

How would I prove sigma r^3?

[@ExamSolutions_Maths]

Cool

[@jared6893]

I don get iyt

[@oOQubixOo]

is this s1?

[@lavarball61]

great video. but this induction stuff is soooooo longggg

[@persiangulfcat]

ありがとう！

[@tuneese2561]

@*Floofy shibe* thanks mate.

[@mohashifa6286]

Likely

[@kevinklose]

you are awesome

[@_stormmz]

Team watching before exam😎✌🏽

[@BorisMediaProds]

You kind of sound like Raoul Silva from skyfall.

[@thatomofolo452]

I can do it 💪

[@elitegamer95]

Story Bro

[@andrewe9527]

okay callux

[@faithelias2798]

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[@sheshanfernando-uv1uj]

Pulling out 1/6 was not right