+0  
 
0
41
2
avatar+25 

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

 
OldTimer  Jan 10, 2018
Sort: 

1+0 Answers

 #1
avatar+91451 
0

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.

 
Melody  Jan 10, 2018

11 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details