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#1 2013-08-15 12:52:46

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

hockey stick identity proof

In class we studied the identity \displaystyle\binom{r}{r}+\binom{r+1}{r} +\binom{r+2}{r} + \cdots +\binom{n}{r} = \binom{n+1}{r+1} We also took a glimpse at \displaystyle\binom{r}{0}+\binom{r+1}{1} +\binom{r+2}{2} + \cdots +\binom{n}{n-r} = \binom{n+1}{n-r}. We will now take a closer look at this second identity.

(a) Confirm that the second identity works for n=5, r=2 and for n=7, r=3.

(b) What is the relationship between the first and second identities?

(c) Prove the second identity above algebraically without using what you learned in Part b. (In other words, prove it without the help of the hockey stick identity we studied in class).

(d) Prove the second identity above with a block-walking argument.


Genius is one percent inspiration and ninety-nine percent perspiration

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#2 2013-08-15 19:20:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

Hi;

Sorry, I can not read that?!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-08-16 05:13:28

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

srry, i used latex, i will change it to regular english


Genius is one percent inspiration and ninety-nine percent perspiration

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#4 2013-08-16 05:16:37

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

In class we studied the identity combination{r}{r}+combination{r+1}{r} +combination{r+2}{r} + ... +combination{n}{r} = combination{n+1}{r+1} We also took a glimpse at combination{r}{0}+combination{r+1}{1} +combination{r+2}{2} +... +combination{n}{n-r} = combination{n+1}{n-r}. We will now take a closer look at this second identity.

(a) Confirm that the second identity works for n=5, r=2 and for n=7, r=3.

(b) What is the relationship between the first and second identities?

(c) Prove the second identity above algebraically without using what you learned in Part b. (In other words, prove it without the help of the hockey stick identity we studied in class).

(d) Prove the second identity above with a block-walking argument.


Genius is one percent inspiration and ninety-nine percent perspiration

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#5 2013-08-16 05:17:51

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

combination{x}{y} means x combination y


Genius is one percent inspiration and ninety-nine percent perspiration

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#6 2013-08-16 05:25:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

I know that.

combination{r}{r}+combination{r+1}{r} +combination{r+2}{r} + ... +combination{n}{r} = combination{n+1}{r+1} We also took a glimpse at combination{r}{0}+combination{r+1}{1} +combination{r+2}{2} +... +combination{n}{n-r} = combination{n+1}{n-r}.

It is totally unreadable on my browser


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#7 2013-08-17 04:45:44

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

i will change it


Genius is one percent inspiration and ninety-nine percent perspiration

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#8 2013-08-17 04:51:53

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

In class we studied the identity (r) combination (r) + (r+1) combination (r) +(r+2) combination (r) + ... + (n) combination (r) = (n+1) combination r+1 We also took a glimpse at (r) combination (0) + (r+1) combination (1) +(r+2) combination (2) +... +(n) combination (n-r) = (n+1) combination (n-r). We will now take a closer look at this second identity.

(a) Confirm that the second identity works for n=5, r=2 and for n=7, r=3.

(b) What is the relationship between the first and second identities?

(c) Prove the second identity above algebraically without using what you learned in Part b. (In other words, prove it without the help of the hockey stick identity we studied in class).

(d) Prove the second identity above with a block-walking argument.


Genius is one percent inspiration and ninety-nine percent perspiration

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#9 2013-08-17 04:55:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

Hi;

What was your answer for a)?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#10 2013-08-17 11:41:29

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

i didn't know how to do it


Genius is one percent inspiration and ninety-nine percent perspiration

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#11 2013-08-17 13:37:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

Hi;

Did you substitute the values in?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#12 2013-08-21 12:15:22

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

i think i got it


Genius is one percent inspiration and ninety-nine percent perspiration

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#13 2013-08-21 12:16:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

Very good!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#14 2013-08-21 12:16:29

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

never mind i didn't get it


Genius is one percent inspiration and ninety-nine percent perspiration

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#15 2013-08-21 12:18:08

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

how do you substitute it


Genius is one percent inspiration and ninety-nine percent perspiration

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#16 2013-08-21 12:45:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

We also took a glimpse at (r) combination (0) + (r+1) combination (1) +(r+2) combination (2) +... +(n) combination (n-r) = (n+1) combination (n-r).

You want to prove this identity for n=5, r=2 and for n=7, r=3?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#17 2013-08-23 15:44:21

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: hockey stick identity proof

yes please, but i don't know how to


Genius is one percent inspiration and ninety-nine percent perspiration

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#18 2013-08-23 16:58:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,507

Re: hockey stick identity proof

As near as I can understand it, for n=5, r=2.

We are done.

For n=7, r=3.


We are done.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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