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Prove by combinatorial argument that .^(...

Prove by combinatorial argument that `.^(n+1)C_r=^n C_r+^n C_(r-1)dot`

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Prove that combinatorial argument that ^n+1C_r=^n C_r+^n C_(r-1)dot

If 1lt=rlt=n , then \ n^(n-1)C_r_ _1 =(n-r+1)\ ^n C_(r-1)dot

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

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

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

Let n\ a n d\ r be no negative integers suych that rlt=n .Then, \ ^n C_r+\ ^n C_(r-1)=\ ^(n+1)C_r

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

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

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

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))

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