- #1
gimpy
- 28
- 0
Hi, I am having a little trouble with this proof:
Let n be a positive integer. What is the largest binomial coefficient [tex]C(n,r)[/tex] where r is a nonnegative integer less than or equal to n? Prove your answer is correct.
So let [tex]r = \lfloor{\frac{n}{2}\rfloor} [/tex] or [tex]r = \lceil{\frac{n}{2}\rceil} [/tex] then [tex]\left( \begin{array}{c} n \\ r \end{array} \right)[/tex] is the largest binomial coefficient.
Now I am having trouble with the proof. Where do i begin?
Maybe something like this?
[tex]\left( \begin{array}{c} n \\ \lfloor \frac{n}{2} \rfloor \end{array} \right) = \frac{n!}{\left(\lfloor \frac{n}{2} \rfloor \right)! \left(n - \lfloor \frac{n}{2} \rfloor \right)!} = ...[/tex]
Am i on the right track?
Let n be a positive integer. What is the largest binomial coefficient [tex]C(n,r)[/tex] where r is a nonnegative integer less than or equal to n? Prove your answer is correct.
So let [tex]r = \lfloor{\frac{n}{2}\rfloor} [/tex] or [tex]r = \lceil{\frac{n}{2}\rceil} [/tex] then [tex]\left( \begin{array}{c} n \\ r \end{array} \right)[/tex] is the largest binomial coefficient.
Now I am having trouble with the proof. Where do i begin?
Maybe something like this?
[tex]\left( \begin{array}{c} n \\ \lfloor \frac{n}{2} \rfloor \end{array} \right) = \frac{n!}{\left(\lfloor \frac{n}{2} \rfloor \right)! \left(n - \lfloor \frac{n}{2} \rfloor \right)!} = ...[/tex]
Am i on the right track?