Anybody wana help me prove this formula?

[Deagle]

Ok this is an extra credit assignment for my AlgII class. I'm getting a B+ right now.:( :eek: Show me how to get from this: (ignore the lines)
___n
<b>(SIGMA)</b> i^2 = (1^2)+(2^2)+(3^2)...+(n^2)
__i=1

to this =n(n+1)(2n+1)
____________6

Thanx I really need this grade :D

[jeeza]

As a hint and to get you started : there are n terms in that addition, aren't there ?
That means you can factor out n from that addition, so you are getting this closer to your second expression.

[Deagle]

Yes there's n terms in that addition. I didn't get what you mean by factoring out n. How would I do that?
Thanx:)

[jeeza]

Actually I am not too sure myself, but as there are n terms in that addition, you can also put it as : n times "something".
That "something" is not something fixed, it is variable as each of these terms has a different value.
But as you see from the end result (the product), that "something" is expressed as as product of two expressions with the parameter n.
So it is possible to express that "something". It's a matter of finding a way.

I suggest you take a look <a href="http://mathworld.wolfram.com">here</a>.
You can also look in <a href="http://dir.yahoo.com/Science/Mathematics">Yahoo's directory</a> and narrow-down further, or take a look at the sites mentioned.

Otherwise, I am sure there are greater math specialists than I am on this board, or they might just cut-n-paste the object of your desire.

[john5211]

I'm not sure what your teacher had in mind, but this is easy enough to prove using induction. If you've never heard of this before, have a look here (http://www.cc.gatech.edu/people/home/idris/AlgorithmsProject/ProofMethods/Induction/UnderstandingInduction.html), or just do a google search on 'mathematical induction.'

Of course, you might want to check with your instructor and see if that's what they had in mind before you sink too much time into it ...

Good Luck,
John

[jeeza]

Originally posted by Deagle
Ok this is an extra credit assignment for my AlgII class. I'm getting a B+ right now.:( :eek: Show me how to get from this: (ignore the lines)
___n
<b>(SIGMA)</b> i^2 = (1^2)+(2^2)+(3^2)...+(n^2)
__i=1

to this =n(n+1)(2n+1)
____________6

Thanx I really need this grade :D
Deagle,
As it is not clear from your post ; with your second expression, do you mean this :

n(n+1)(2n+1) / 6

[john5211]

So I certainly hope I'm not stepping on Deagle's toes, but here is a picture of the equation/problem that Deagle posed at the beginning of the thread (although I just noticed that his indices run from i=1 to n instead of i=0 to n ... it doesn't make a difference in this case, though):

http://netfiles.uiuc.edu/jbutler1/www/EQN1.jpg


Another problem that uses the same concepts but has slightly easier algebra is: Prove the following:

http://netfiles.uiuc.edu/jbutler1/www/EQN2.jpg


John

[Deagle]

Thanx John, the 1st picture is what I'm trying to say except it's i=1 instead of 0. I have already prove the 2nd formula so there's no need for that.:cool:
:)

[Deagle]

Any idea so far?:(

[john5211]

Well, where exactly are you stuck? (I don't mean to sound mean, I just need a better idea of what you have tried so far to offer many useful suggestions.)

I guess the most general suggestion is that you want to prove this equation the same way you proved the other one that I posted above. Of course some of the details will be a little different, but the ideas and the general steps are exactly the same.

If that doesn't help you any, post back with what you have tried so far and maybe I can offer a better suggestion.

Good Luck,
John

[Deagle]

I tried to do it like how I proved the first equation but to no avail. I search the web and found this. This is the step right before finalization.

[john5211]

Hi Deagle,

Well, I'm still not sure exactly where you are getting stuck, but like I said, the way to do the proof is to emulate the method used in the proof of the other example. To illustrate what I mean, I've written up a quick solution to the other problem and posted it on the web (here (http://netfiles.uiuc.edu/jbutler1/www/induction.html)).

Hopefully if you look over it you will see that there are two steps you need to take to solve your current problem (the same two steps one always takes when solving a problem by induction). Of course, much of the algebra will be different (and harder) with your current problem, but the two steps I highlighted are the two steps you need to take to solve the problem.

Of course feel free to ask any further questions, and good luck!

John

[deddard]

Is anyone else getting a link to a a secure site when they click on this thread?

If I click on this thread, or when I initiated this reply, I got a pop-up box saying I was going to a secure site. No site actually appears, but my firewall log shows the site as:
10:12:46 iexplore.exe TCP netfiles.uiuc.edu HTTP Internet explorer HTTP connection

Entering this site into explorer comes up with the site CITES NetFiles.uiuc.edu
and is directed to https://netfiles.uiuc.edu/xythoswfs/webui

The site is a log-in page, with the following:

NetID:


Active Directory Password:

Persistent Session Cookie?


CITES NetFiles Documentation
Vendor Documentation
Change AD Password

The additional site info gives:

Guide to CITES NetFiles
CITES > CITES NetFiles Index
CITES NetFiles is a service that allows University faculty, staff, and students to access their files from anywhere in the world. You can use NetFiles from a web browser or from client software that you set up on your PC, Mac or Unix/Linux workstation.
Your NetFiles account will be set up to allow web publishing in a single step. CITES NetFiles also includes a number of features designed to facilitate collaboration. You can, for instance, define groups that you want to have access to specific files or create dropboxes for students to hand in homework.

NetFiles is an ideal application for storing files you need to access from a number of different locations (e.g., home, desktop workstations, campus computer labs, and even while traveling). Because it provides a secure, central access point, NetFiles is perfect for backing up critical files and data.

[YODA74]

deddard
If your talking about johns link just view soucr you'll see an addy there paste it into your browser should get W3C home directory

http://www.w3.org/Math/

http://www.w3.org/

[deddard]

I think that's what it must be.
I didn't actually click on any of john's links when the secure site dialogue box popped up though; I simply went from the After Hours Club to this thread, and I was immediately presented with the secure connection box.
I blocked the site (the one the https was directing to) in my firewall, and now when I click on this thread, I don't get the secure site dialogue, and john's links are blanked out - a bit weird, but I just thought something a bit fishy was happening as I hadn't actually clicked anything.

[john5211]

Did you get just an information box or did you get a logon prompt?

You might at least get an information box just by clicking on the thread because the images I posted at the beginning of the thread (two equations) are hosted on a secure site. (So is the link, but of course that doesn't matter if you don't click on it). But I'd be interested to know if you actually got a login prompt (that obviously shouldn't happen).

Sorry for any confusion,
John

[deddard]

No, there was no logon prompt, just the dialogue box informing me that i was being redirected to a secure site. I hadn't come across this on this site before, so I just thought it was a bit strange.