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October 15th, 2012, 10:23 AM   #1
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sum of integers squared

i have been searching for a formula for this but i could only find one for the sum of the first n integers squared which was

now i have been producing a formula that can calculate the sum of integers squared no matter where you start or the difference between the integers.
i became:

so for example if you want to calculate you have to do:






is this anything special or anything new that might be usefull. please comment.
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October 15th, 2012, 11:32 AM   #2
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Re: sum of integers squared

If the sum of the squares of the first n positive integers is f(n), then the sum of the squares of k+1, k+2, ..., n is f(n) - f(k). Concretely:

(2n^3 + 3n^2 + n - 2k^3 - 3k^2 - k)/6
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October 15th, 2012, 01:15 PM   #3
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Re: sum of integers squared

Hello, gelatine1!

Quote:
I have been searching for a formula for this,
but i could only find one for the sum of the first n integers squared
which was:

Now i have been producing a formula that can calculate the sum of integers squared,
no matter where you start or the difference between the integers.

With a constant difference between the integers, we have an arithmetic sequence.








[color=beige]. . . [/color]




[color=beige]. . . . [/color]

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October 15th, 2012, 06:23 PM   #4
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Re: sum of integers squared

Quote:
Originally Posted by gelatine1
i have been searching for a formula for this but i could only find one for the sum of the first n integers squared which was

now i have been producing a formula that can calculate the sum of integers squared no matter where you start or the difference between the integers.
i became:

so for example if you want to calculate you have to do:






is this anything special or anything new that might be usefull. please comment.
I think your formula is elegant, i've never seen it before, but i am not an expert and i have never had anything published of any consequence. I have published problems and solutions in School Science and Mathematics Association journal, editor, Ted Eisenberg.

http://www.ssma.org/publications

Read this link carefully and look at previous issues and problem proposal publications. If you can write up an article, maybe Mr. Eisenberg will publish it, although i suspect it is harder to publish articles, you may need credentials, but almost anyone can propose a problem.

Here is a possible approach, you send Ted Eisenberg your formula along with a numerical example, if you have a proof, send that too, you ask him to put it in the problem section of the journal, something like 'prove the following formula for the sum of n consecutive squares of integers with common difference starting at any integer square' or you may have a better title. Ted puts it in the journal, along with your name as proposer. Mathematicians all over the world see it and work on it, send in solutions. A few months after proposal, Ted publishes the best solution and mentions every name that sent in correct solutions.

I don't know how many mathematicians read this journal but it's got to be at least thousands of professionals worldwide so you will get some glory which you can use in a resume.

Like i said, i don't know how important your formula is, so i don't know if i'm giving you sound advice, you have to decide for yourself. In my opinion, Ted Eisenberg will put it in the journal.

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October 15th, 2012, 09:59 PM   #5
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Re: sum of integers squared

i will give it a try.
i just have to send a mail to for that ? or is there something on the site for that?
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October 16th, 2012, 01:12 AM   #6
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Re: sum of integers squared

Does the e-mail link on the site work for you? If it does then click on it and send him an e-mail. I tried it but it's non functioning, but i'm using PS3 to surf the net, PS3 has limitations so when a link doesn't work for me i don't know if the problem is on my end or the other end.

You can write up your problem proposal and fax it to him, +972-86-477-648, (not sure about the + for faxes but you need it for international phone calls) Put your phone number, ask him to respond, ask him for his phone number so you can talk to him. Make sure you put in the fax it's a problem proposal for SSMA journal. He's a professor at Ben-Gurion University in Beer-Sheva Israel and has an office there, the number is public knowledge so i think i can post it here, +972-8-647-7800 Try calling him. You may have to figure out time zones since he's in Israel.

If all else fails, you can send it to him by regular mail, his address is at the first link i gave in my first post.

Here is Ben-Gurion University website

http://www.math.bgu.ac.il/

Here is faculty directory with his info (13th from top)

http://www.math.bgu.ac.il/people/faculty.html

Let me know if you have other questions and how it all turns out.



[EDIT]* I haven't made an international phone call in 20 years so i don't know about + signs [ENDEDIT]
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October 16th, 2012, 11:22 AM   #7
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Re: sum of integers squared

I've sent a huge email to him now I will let you know if he replies something.
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