[quad D_(r)=|[1,n,n],[2r,n^(2)+n+1,n^(2)+n],[2r-1,n^(2),n^(2)+n+1]|],[" If "],[" then "n" is equal to "],[0,4],[0,6],[0,8],[0,7]D_(r=1)^(n)D_(r)=56

If D_r=|[r,1,(n(n+1))/(2)],[2r-1,4,n^2],[2^(r-1),5,2^(n)-1]| then, sum_(r=1)^n D_r

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

If D_(r)=|(r,x,n(n+1)//2),(2r-1,y,n^(2)),(3r-1,z,n(3n+1)//2)| then sum_(r=1)^(n)D_(r)=

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If n in N, then sum_(r=0)^(n) (-1)^(n) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

If n in N, then sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

If for any +ve integer n Delta_(n)=[[2r-1,^(n)C_(r),1n^(2)-1,2^(n),n+1cos^(2)(n^(2)),cos^(2)(n),cos^(2)(n+1)] then sum_(r=0)^(n)Delta_(r),n in N, is equal to