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

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

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

If ""(n)C_(r) denotes the number of combinations of n different things taken r at a time, then the vlaue of ""^(n)C_(r+1)+""^(n)C_(r-1) + 2. ""^(n) C_(r) is-

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))

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

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

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

If ""^(n)C _r denotes the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C_(r+1)