- #1

VinnyCee

- 489

- 0

## Homework Statement

Show that if n is a positive integer, then [tex]1\,=\,\binom{n}{0}\,<\,\binom{n}{1}\,<\,\cdots\,<\,\binom{n}{\lfloor\frac{n}{2}\rfloor}\,=\,\binom{n}{\lceil\frac{n}{2}\rceil}\,>\,\cdots\,>\binom{n}{n\,-\,1}\,>\,\,\binom{n}{n}\,=\,1[/tex]

## Homework Equations

I think this proof involves corollary 2 of the Binomial Theorem.

[tex]\sum_{k\,=\,0}^n\,(-1)^k\,\binom{n}{k}\,=\,0[/tex]

## The Attempt at a Solution

I have NO idea where to start a proof of this sort. This problem is labeled as 'easy', but I don't see the easiness yet. I know that an attempt at a solution is required before any assistance is rendered, but I have been staring at (and thinking about) this problem for two days now. I can't think of ANYTHING that is even remotely helping me to "show" this theorem.

I am not trying to have someone else do my homework or anything like that, I just need a pointer or two. If you don't believe me, look at my previous threads, all have detailed attempts and most were completed problems after help was given.

Thanks for your help in advance.

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