SOLUTION: nc1+2nc2+3nc3+...+nncn

Question 1080977: nc1+2nc2+3nc3+...+nncn
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
nc1+2nc2+3nc3+...+nncn
~~~~~~~~~~~~~~~~~

The sum is 

Sum =  +  +  + . . . + .


The common term is

 =  =  =  = .

Therefore,

Sum =  +  +  + . . . +  =  +  +  + . . .  = .

It is widely known (*) that 

 = .   (*)

Hence,

Sum = .


Regarding the statement (*) see the lesson
    Remarkable identities for Binomial Coefficients 
in this site.

Solved.

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