Binomail Theorem!! (1 Viewer)

[EvoRevolution]

 

[Timothy.Siu]

well,

RHS=(1+x)^m (1+3x^2+3x+x^3)

so, equating the coefficients of x^r
we get that .

 

[addikaye03]

LHS=mC0+mC1(x)+mC2(x^2)+...+m+3Cr (x^r)
RHS=[(1+x)^m=mC0+mC1(x)+mC2(x^2)+...+mCr-3 (x^r-3)+mCr-2(x^r-2)+mCr(x^r-1)+mCr(x^r)]((1+3x^2+3x+x^3)

By comparing coefficients of x^r,

m+3Cr=mCr+3(mCr-1)+3(mCr-2)+mCr-3 #

Edit: Wish i saw your post Tim, i would have never done any of that lol

 

[Timothy.Siu]

LHS=mC0+mC1(x)+mC2(x^2)+...+m+3Cr (x^r)
RHS=[(1+x)^m=mC0+mC1(x)+mC2(x^2)+...+mCr-3 (x^r-3)+mCr-2(x^r-2)+mCr(x^r-1)+mCr(x^r)]((1+3x^2+3x+x^3)

By comparing coefficients of x^r,

m+3Cr=mCr+3(mCr-1)+3(mCr-2)+mCr-3 #

Edit: Wish i saw your post Tim, i would have never done any of that lol

nah didn't u do it right? i just cudn't be bothered to write out working lol

 

[addikaye03]

nah didn't u do it right? i just cudn't be bothered to write out working lol

haha yer i suppose, but i mean you summarised it all pretty nicely haha