Proving the Binomial Theorem: Simplifying Binomial Coefficients

[dalarev]

Homework Statement

Show that binomial coefficients $$\frac{-1}{n}$$ = (-1)$$^{n}$$

Homework Equations

(1+x)^p = (p / n) x^n

The Attempt at a Solution

I'm clueless on the idea of binomial coefficients. I think if I understood the question better I'd know at least where to start. It's not actually -1/n (no division) but I couldn't find the right syntax for it.

 

[jjou]

I think your equation for (1+x)^p is incomplete. There should be a summation of p+1 terms on the right hand side.

Also, there is a lot of information on binomial coefficients, binomial expansion, and even a formula for generalization to negative numbers on Wikipedia, which should be very helpful.

 

[HallsofIvy]

The binomial theorem says that
$$(a+ b)^n= \sum_{i= 0}^n\left(\begin{array}{c} n \\ i \end{array}\right)a^{n-i}b^i$$
is that what you mean? And please do not use (p/n) for the binomial coefficient! That's extremely confusing. If you don't want to use LaTex, use nCi.

 

[dalarev]

The binomial theorem says that
$$(a+ b)^n= \sum_{i= 0}^n\left(\begin{array}{c} n \\ i \end{array}\right)a^{n-i}b^i$$
is that what you mean? And please do not use (p/n) for the binomial coefficient! That's extremely confusing. If you don't want to use LaTex, use nCi.

yes, that's what I meant. I'm not very experienced with math type on this forum.