Summation Proof with Binomial Theorem

ChaoticLlama

Prove the following statement:

[tex]\[
\sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c}
n + r - 1 \\
r \\
\end{array} \right)} \left( \begin{array}{c}
m \\
s \\
\end{array} \right) = \left( \begin{array}{c}
m - n \\
t \\
\end{array} \right)
\]
[/tex]

Any initial help is appreciated.

cristo

Well, what have you done? What is the definition of, say, m choose s?

Similar Threads for: Summation Proof with Binomial Theorem
Thread	Forum	Replies
Connection between cubed binomial and summation formula proof (for squares)...	Precalculus Mathematics Homework	5
DISCRETE MATH: Binomial Theorem proof (using Corollary 2)	Calculus & Beyond Homework	6
Can you check my proof, (binomial theorem appplied)	Calculus & Beyond Homework	1
binomial theorem	Precalculus Mathematics Homework	15
Proof of the binomial theorem	General Math	9

ChaoticLlama	Summation Proof with Binomial Theorem Tweet Prove the following statement: [tex]\[ \sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c} n + r - 1 \\ r \\ \end{array} \right)} \left( \begin{array}{c} m \\ s \\ \end{array} \right) = \left( \begin{array}{c} m - n \\ t \\ \end{array} \right) \] [/tex] Any initial help is appreciated.

cristo Mentor	Well, what have you done? What is the definition of, say, m choose s?