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" A.(i) Prove that "^(n)C(r)-:^(n-1)C(r-...

" A.(i) Prove that "^(n)C_(r)-:^(n-1)C_(r-1)=(n)/(r)

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Prove that .^(n)C_(r)+^(n)C_(r-1)=^(n+1)C_(r)

Prove that ""^(n)C_(r)+""^(n)C_(r-1)=""^(n+1)C_(r) .

Prove that ""^(n)C_r + ""^(n)C_(r-1) = ""^(n+1)C_r

Prove that n.^(n-1)C_(r-1)=(n-r-1) ^nC_(r-1)

Prove that : (""^(n)C_(r+1))/(""^(n)C_(r))=(n-r)/(r+1)

Prove that : (""^(n)C_(r+1))/(""^(n)C_(r))=(n-r)/(r+1)

Prove that (r+1)^(n)C_(r)-r^(n)C_(r)+(r-1)^(n)C_(2)-^(n)C_(3)+...+(-1)^(r)n_(C_(r))=(-1)^(r_(n-2))C_(r)

Prove that ""^(n)C_(r )+2""^(n)C_(r-1)+ ""^(n)C_(r-2)= ""^(n+2)C_(r ) .

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

Prove that ""^(n+1)C_(r+1)=(n+1)/(r+1)"^nC_r