A community for students.
Here's the question you clicked on:
 0 viewing
swissgirl
 3 years ago
Give a combinatorial proof of Vandemonde's identity, for x, a, n ∈ ℕ
Look at image below
where ( ⋅ ) denotes the binomial coefficient nCr.
swissgirl
 3 years ago
Give a combinatorial proof of Vandemonde's identity, for x, a, n ∈ ℕ Look at image below where ( ⋅ ) denotes the binomial coefficient nCr.

This Question is Closed

NotTim
 3 years ago
Best ResponseYou've already chosen the best response.0ottawa u. is that a university in those canada regions?

NotTim
 3 years ago
Best ResponseYou've already chosen the best response.0unless you want us to hack.

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0ohhh s*** okkk give me a sec

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0alrighty here is the image

NotTim
 3 years ago
Best ResponseYou've already chosen the best response.0please some1 else be able to do this...

Valpey
 3 years ago
Best ResponseYou've already chosen the best response.2\[\dbinom{x+a}{n}=\sum_{k=0}^n{\dbinom{x}{k}\dbinom{a}{nk}}\] \[\sum_{k=0}^n{\dbinom{x}{k}\dbinom{a}{nk}}=\dbinom{x}{0}\dbinom{a}{n0}+\dbinom{x}{1}\dbinom{a}{n1}+\dbinom{x}{2}\dbinom{a}{n2}+...\] \[+\dbinom{x}{n}\dbinom{a}{0}\]

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0What rules did u use?

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1easier method http://en.wikipedia.org/wiki/Vandermonde's_identity#Combinatorial_proof

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0hahahahahah nahhhh both u guys win ok ill medal valpey and valpey medals experimentx

Valpey
 3 years ago
Best ResponseYou've already chosen the best response.2The tricky part is the leap from: \[\left(\sum_{i=0}^{m}\dbinom{m}{i}x^i\right)\left(\sum_{j=0}^{n}\dbinom{n}{j}x^j\right)=\sum_{r=0}^{m+n}\left(\sum_{k=0}^{r}\dbinom{m}{k}\dbinom{n}{rk}\right)x^r\] It is helpful to think of these terms as the diagonals of an m x n matrix of terms where each diagonal i+j=r.

Valpey
 3 years ago
Best ResponseYou've already chosen the best response.2But the proof using Democrats and Republicans in the US Senate works for me.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.