Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 105625 by  M±th+et+s last updated on 30/Jul/20

prove that   ((m),(m) ) (((   n)),((n−k)) )+ (((    m)),((m−1)) ) (((       n)),((n−k+1)) )  + (((   m)),((m−2)) ) (((        n)),((n−k+2)) )+......+ (((    m)),((m−k)) ) ((n),(n) )  = (((m+n)),((     k)) )

provethat(mm)(nnk)+(mm1)(nnk+1)+(mm2)(nnk+2)+......+(mmk)(nn)=(m+nk)

Answered by prakash jain last updated on 30/Jul/20

(1+x)^(m+n) =(1+x)^m (1+x)^n   compare coefficient of x^k  on LHS  and RHS.  LHS=C_k ^(m+n)   RHS  (C_0 ^m x^m +C_1 ^m x^(m−1) +..+C_(m−k) ^m x^k +..+C_m ^m )×  (C_0 ^n x^n +C_1 ^n x^(n−1) +..+C_(n−k) ^n x^k +..+C_n ^n )×  coefficient of x^k   C_m ^m C_(n−k) ^n +..+C_n ^n C_(n−k) ^n

(1+x)m+n=(1+x)m(1+x)ncomparecoefficientofxkonLHSandRHS.LHS=Ckm+nRHS(C0mxm+C1mxm1+..+Cmkmxk+..+Cmm)×(C0nxn+C1nxn1+..+Cnknxk+..+Cnn)×coefficientofxkCmmCnkn+..+CnnCnkn

Terms of Service

Privacy Policy

Contact: info@tinkutara.com