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# Summation watch

1. Hello I know that the summation of r^2 from r=1 to r=n is [n(n+1)(2n+1)]/6, but I wasn't able to derive it. My approach was to write it as 1,1+2+1,1+4+4,1+6+9... but it didn't get me anywhere. A bit of aid would be much appreciated.
2. (Original post by Spandy)
Hello I know that the summation of r^2 from r=1 to r=n is [n(n+1)(2n+1)]/6, but I wasn't able to derive it. My approach was to write it as 1,1+2+1,1+4+4,1+6+9... but it didn't get me anywhere. A bit of aid would be much appreciated.
there are several different proofs

e.g induction

or

method of differences with a choice of suitable identities
3. Oh crap, induction had totally slipped out of my mind, thanks!!
4. (Original post by Spandy)
Oh crap, induction had totally slipped out of my mind, thanks!!
my pleasure
5. Do you know how to derive Σk? Whatever method you used for this also applies here!
6. (Original post by NoNewFriends)
Do you know how to derive Σk? Whatever method you used for this also applies here!
No it doesn't

Unless I have completely misunderstood what you are suggesting
7. (Original post by TenOfThem)
No it doesn't

Unless I have completely misunderstood what you are suggesting
You know a lot more than I know so I'm probably wrong but which method do you have in mind that works for Σk but doesn't for Σk²?
8. (Original post by NoNewFriends)
You know a lot more than I know so I'm probably wrong but which method do you have in mind that works for Σk but doesn't for Σk²?
Standard proof for the sum of the first n numbers
9. (Original post by TenOfThem)
Standard proof for the sum of the first n numbers
Which one is the standard one?
10. (Original post by NoNewFriends)
Which one is the standard one?
Write the numbers in reverse
Half
11. (Original post by NoNewFriends)
Which one is the standard one?
Let:

Then
12. (Original post by NoNewFriends)
Which one is the standard one?
Hurrah for Joostan. Or simply use the formula for arithmetic progressions
13. I wrote this a long time back on my website (http://www.whitegroupmaths.com/2010/...hematical.html see Q6), hopefully it helps. Peace.

14. I wrote this a long time back on my website (http://www.whitegroupmaths.com/2010/...hematical.html see Q6), hopefully it helps. Peace.

(Click on the image to enlarge)
15. (Original post by Spandy)
Hurrah for Joostan. Or simply use the formula for arithmetic progressions
You were looking for proof
16. (Original post by TenOfThem)
You were looking for proof
Uhh, I must be drunk.
17. (Original post by WhiteGroupMaths)
I wrote this a long time back on my website (http://www.whitegroupmaths.com/2010/...hematical.html see Q6), hopefully it helps. Peace.
Or similarly but with r(r+1)(r+2) - (r-1)r(r+1) = 3r(r+1).

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