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Question Number 105625 by M±th+et+s last updated on 30/Jul/20
provethat(mm)(nn−k)+(mm−1)(nn−k+1)+(mm−2)(nn−k+2)+......+(mm−k)(nn)=(m+nk)
Answered by prakash jain last updated on 30/Jul/20
(1+x)m+n=(1+x)m(1+x)ncomparecoefficientofxkonLHSandRHS.LHS=Ckm+nRHS(C0mxm+C1mxm−1+..+Cm−kmxk+..+Cmm)×(C0nxn+C1nxn−1+..+Cn−knxk+..+Cnn)×coefficientofxkCmmCn−kn+..+CnnCn−kn
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