PASCAL PYRAMID and MATHEMATICAL INDUCTION

[rappyrap09]

HELP!!!! i need help...

is anyone familiar with PASCAL PYRAMID AND MATHEMATICAL INDUCTION??

[hhemken]

rappyrap09,

What are you looking for, specifically? Have you tried googling this:

Code: Select all

"PASCAL's PYRAMID" AND MATHEMATICAL INDUCTION

There are more than a few hits for that combination of keywords. I suggest you have a look and come back with more specific questions and what your science project might be about.

[rappyrap09]

my project is about PASCAL PYRAMID..but, according to my professor, it can be proved by using MATHEMATICAL INDUCTION.. so i thiin the're related..please help me on this project..

[hhemken]

rappyrap09,

Have you read the materials that come up on Google with the search I suggested? Print some out and discuss them with your professor. I think a one-on-one with your professor discussing specific texts you have both read will be better and faster than posting the discussion here.

Please let us know what you conclude or what additional questions you may have, though.

[rappyrap09]

are you familiar with Pascal Triangle???if yes then you would knnow how pascal pyramid works..

i've just got questions...a formula/ae on how to get a layer without the help of its previous layers..help me..can't find it in google..

and my professor just told me that Pascal Pyramid could be proved by using mathematical induction...this one i can't do..please help..do you have any guidelines on how to prove this Pascal Pyramid...help

[LeungWilley]

Hi Rappyrap09,
Please see if this link is helpful:
http://en.wikipedia.org/wiki/Binomial_coefficient

If I understand what you are trying to do correctly, you may be using induction to prove the recurrence relation of the Pascal Pyramid. The specific are shown in the middle of the article.

Please let us know how it works out.
Good Luck!
Willey

[Goldenzenith]

Hello,

Is this for a math research paper? If so, it would be best to do what the other Experts have suggested and look into the wealth of resources provided. And don't hesitate to consult your teacher for help; you're in school to learn, remember!

As for Pascal's Triangle and mathematical induction, you'll need to know Pascal's Law, which is nCr = n-1Cr + n-1Cr-1. Right now, get a piece of paper and draw at least the first 3 rows of Pascal's Triangle. How can you rewrite each number as a combination? Here's a hint: the first row has 0C0, and the second row has 1C0 and 1C1.

Once you figure out why Pascal's Law makes sense, you can get to work with mathematical induction. Remember to neatly set up each step:
1) Prove that the law works for n = 1.
2) Assume that it works for n = k, where k is greater than or equal to zero.
3) Prove that it works for n = k + 1, using and beginning the proof with the assumption from step 2.

This should be all you need to get to work on your paper. If you have any questions, please ask, but remember to do your research first!

[rappyrap09]

LeungWilley, ive already seen that page..thanx anyways



Goldenzenith, yes, its a research papaer..what i need is to provve Pascal Pyramid with the use of mathematical induction..

[Goldenzenith]

My apologies; I misread what you needed to prove. In that case, tell me what you have gotten up to so far, and perhaps we can work from there!

[rappyrap09]

so far, all ive got is a formula in finding how many terms there are in a pascal pyramid..
what i need is to incorporate mathematical induction into pascal pyramid..please help..

[Goldenzenith]

Hi, rappyrap09,

The following site may be of some interest to you: http://threesixty360.wordpress.com/2009 ... rt-1-of-3/. It's not a reference site, but it does make some observations that are related to your project. Take a look!

This is probably the case, but just to confirm, are you trying to prove that the formula you found works? If so, that's something to work with! You should realize that, by proving it, you would be incorporating mathematical induction into your project on Pascal's Pyramid. Perhaps you could post the formula on here and get advice, step by step. If you don't want to do that (which is also perfectly fine), please familiarize yourself with the format of mathematical induction. You've posted many requests for help concerning induction, so I would just like to make sure that you understand what exactly it entails. Remember one of my earlier posts in this thread?

As for Pascal's Triangle and mathematical induction, you'll need to know Pascal's Law, which is nCr = n-1Cr + n-1Cr-1. Right now, get a piece of paper and draw at least the first 3 rows of Pascal's Triangle. How can you rewrite each number as a combination? Here's a hint: the first row has 0C0, and the second row has 1C0 and 1C1.

Once you figure out why Pascal's Law makes sense, you can get to work with mathematical induction. Remember to neatly set up each step:
1) Prove that the law works for n = 1.
2) Assume that it works for n = k, where k is greater than or equal to zero.
3) Prove that it works for n = k + 1, using and beginning the proof with the assumption from step 2.

Although the topic of the above example is not exactly what you need (Pascal's Triangle, as opposed to something related to Pascal's Pyramid), the overall setup would be the same for the proof that you want to create. If you are confused or would like more information, this site has excellent, clear explanations, as well as a few practice problems: http://www.themathpage.com/aprecalc/mat ... uction.htm.

Once you've got mathematical induction down pat, "draft" a proof for your formula. Then look it over and see if you made any unwarranted assumptions that might make the proof invalid. If you need help with a certain step or get stuck somewhere, post your question, but make sure it's a specific one! It's a bit difficult to answer less specific ones like,

my project is about PASCAL PYRAMID..but, according to my professor, it can be proved by using MATHEMATICAL INDUCTION.. so i thiin the're related..please help me on this project..

Please try to provide as many details as you can so that the Experts on Science Buddies can help you better! With that said, good luck with your project, and above all, have fun!

-RM