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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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2013-08-16 05:13:28
- mathstudent2000
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- 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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#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
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- 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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: hockey stick identity proof
Very good!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#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
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- 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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
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