+239 If n Cr, denotes the coefficient of xr in the expansion of (1 + x) n, prove that:
n Cr + 2(n Cr+1) + n Cr+2 = n+2 Cr+2
+118608 Hi Old timer,
This is not a proof, ... I just wanted to convince myself that your statement was true.
I considered Pascals triangle which gives the coefficients nCr
Just considering how the pattern works it can be deduced that
nCr+nCr+1 = n+1Cr+1 and nCr+1+nCr+2 = n+1Cr+2
and
n+1Cr+1 + n+1Cr+2 = n+2Cr+2
so
nCr+nCr+1 + nCr+1+nCr+2 = n+2Cr+2
hence
nCr+ 2nCr+1 +nCr+2 = n+2Cr+2
To prove it I would probably use the fact that nCr = n! /(r! * (n-r)! )
But I will admit that I have not worked through this proof.
