Proof by Induction : Sum of series ∑r² | ExamSolutions
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- čas přidán 25. 03. 2012
- Here you are shown how to prove by mathematical induction the sum of the series for r squared. ∑r²
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10 years later and this goat is still carrying further maths
thats a very straight line.
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.
You sir are a genius! This video is flawless and helped me grasp the concept in one go! Thanks a lot!
Pleased to hear it helped.
OH MY GOD THANK YOU. Exam tomorrow - why didn't I discover this earlier!? Better late than never though, thank you so much!
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
+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 :(
7 years later, and my exam is 2 days away, I hope y'all are having a good life ✌✌@@jamescopland2649
A huge help. Thanks for the clear explanation. FINALLY understand each step.
Immensely helpful, thank you. I was missing a step the textbook just didn't explain well.
Great explanation! This was really easy to follow and understand.
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...)
The exam solutions guy is an absolute lad!
Thank you
Now i really understand the topic
Great one sir
this helped so much!!
Thank you
This helps alot🥰
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.
+TheGminister That's good
Can you do more of these Proof by Mathematical induction videos?
Teaching and learning here is good
Thank you I appreciate thos
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 :)
Very clear, thank you
+liam chandler Thank you
this was helpful
I really appreciate your teaching Sir, l'm a step ahead. Thank you.
I appreciate your comment, thank you.
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..
hey.....what about 7+10+13+16+....+(3n+4)=n/2(3n+11).....what would the k+1 be?
This seems to be a very hard concept for people to explain. I applaud you for doing a great job at explaining it clearly
you are awesome
I do not see where you get 1/6th from both sides the addition sign.
I've been struggling with this problem to find our that my only mistake was that I forgot to square (k+1)....
How would I prove sigma r^3?
I would have thought so.
Good luck
great video. but this induction stuff is soooooo longggg
Cool
If you hate proof by induction put your thumbs up
is this s1?
ありがとう！
@*Floofy shibe* thanks mate.
You kind of sound like Raoul Silva from skyfall.
Likely
No, FP1
I don get iyt
Check out my website. It is on there.
Story Bro
okay callux
Pulling out 1/6 was not right
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