C2 binomial coefficients

redrose_ftw

meant to be simple but i cant do it :/ okay
find the coefficient of x^-12 in the expansion of (x^3 - 1/x)^24
Help?

Reply 1

Ninjasocks

redrose_ftw

meant to be simple but i cant do it :/ okay
find the coefficient of x^-12 in the expansion of (x^3 - 1/x)^24
Help?

http://en.wikipedia.org/wiki/Pascal%27s_triangle

Pascal's triangle determines the coefficients which arise in binomial expansions. For an example, consider the expansion

(x + y)2 = x2 + 2xy + y2 = 1x2y0 + 2x1y1 + 1x0y2.

Notice the coefficients are the numbers in row two of Pascal's triangle: 1, 2, 1. In general, when a binomial like x + y is raised to a positive integer power we have:

(x + y).n =

see wiki cannot parse latex

Unparseable latex formula:

+ ; + a.n−1\;x.y.n−1 + \text{any n,}

where the coefficients ai in this expansion are precisely the numbers on row n of Pascal's triangle. In other words,

a_i = {n \choose i}.

Reply 2

ghostwalker

Ninjasocks

....

If you want superscripts in LaTex, just prefix the symbol with "^", and if there is more than one character put them in braces, thus ^{n-1}.

Similarly for subscripts, use "_"

Reply 3

redrose_ftw

ye i understand all that but i'm not looking to expand it just find the coefficient which i really don't understand :s-smilie:

there is this formula n!/r!(n-r)! will that work in this case

Reply 4

Ninjasocks

ghostwalker

If you want superscripts in LaTex, just prefix the symbol with "^", and if there is more than one character put them in braces, thus ^{n-1}.

Similarly for subscripts, use "_"

Thanks my latex is awfully rusty atm.