Let `n\ a n d\ r` be non negative integers such that `1lt=rlt=ndot` Then, `\ ^n C_r=n/rdot\ \ ^(n-1)C_(r-1)\ dot`

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

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

If m,n,r are positive integers such that r lt m,n, then ""^(m)C_(r)+""^(m)C_(r-1)""^(n)C_(1)+""^(m)C_(r-2)""^(n)C_(2)+...+ ""^(m)C_(1)""^(n)C_(r-1)+""^(n)C_(r) equals

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

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

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

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

Assertion: If n is an even positive integer n then sum_(r=0)^n ("^nC_r)/(r+1) = (2^(n+1)-1)/(n+1) , Reason : sum_(r=0)^n ("^nC_r)/(r+1) x^r = ((1+x)^(n+1)-1)/(n+1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If n is a positive integer and C_r = ""^nC_r then find the value of sum_(x = 1)^n r^2 ((C_r)/(C_(r - 1)) )

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