3rd Level of degree. Can't understand simple maths.


Anyway we all know the binomial theorem for things like (x+y)^7. It tells us what the coefficients of the values will be, we normally just use a calculator (7c0) for x^7, (7c1) for x^6*y, 7c2 for x^5*y^2. ect....until we get all the coefficients. (where 'c' stand for choose, done using the nCr button on a calculator)

Now I am using it to the power of m. My lecturer has said

(x+y)^m = x^m + m*x^(m-1)*y + ([m(m-1)]/2)*x^(m-2) y^2 + .....


As you can see he has shown a pattern in finding the coefficients . (For example if you subbed m=7 into it you'd get 21x^5y^2 as requierd). I cannot spot how this formula continues though. I need to find what coefficient comes next after m(m-1)/2... Just because it's driving me crazy really.

Can anyone spot the pattern that I cannot, things like this do come up on the exam and I can't rely on my nCr calculator button unfortunately. All the websites like Wiki display the solutions in terms of the choose button, which is exactly what I do not want.

http://en.wikipedia.org/wiki/NCr ?

So m(m-1)(m-2)/6.

Unfortunately, I don't think I can usefully advise on spontaneously coming up with patterns in an exam situation however - other than trying out some examples and seeing what fits.

That'll do, you have to find the solution to a certain 'degree' and i doubt it'll be any bigger than that, most of the time it's 4m-5 so any bigger you can ignore, thanks for that.

Knew I should have done combinatorics!