Thread: more binomials

I cannot figure out how to simplify binomials. (i) i can do (ii) i cant

(i) write down the general term in the expansion of

(ii) use the term

to prove that: (this is binomials btw)

mCr+mCr-1.nC1+mCr-2.nC2+....+nCr=n+mCr where . is a multiple sign

Originally Posted by oxrigby

I cannot figure out how to simplify binomials. (i) i can do (ii) i cant

(i) write down the general term in the expansion of

(ii) use the term

to prove that: (this is binomials btw)

mCr+mCr-1.nC1+mCr-2.nC2+....+nCr=n+mCr where . is a multiple sign

.... (1)

.... (2)

Partially expand (2) to get the coefficient of :



Compare this with the coefficient of given in (1).

how do you partially expand this? D o you just take into account the first three terms in each bracket i.e 1,nC1x,nCrx^r multiply them together,equate them to (1+x)^n+m. Im also confused by the notation of r and s shouldn't it just be one of them''..

Originally Posted by oxrigby

how do you partially expand this? D o you just take into account the first three terms in each bracket i.e 1,nC1x,nCrx^r multiply them together,equate them to (1+x)^n+m. Im also confused by the notation of r and s shouldn't it just be one of them''..

Multiply out the terms that you can see will give you a coefficient of x^r. You might want to include more terms in each of the brackets than I did to help you see this.