If `Delta_r =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1, 3^n-1, 5^n-1]|` , then find the value of `Delta`

If Delta_r=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

If "Delta"_r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, 5^n-1]| Show that sum_(r=1)^n"Delta"_r = Constant

if Delta_r=|[x,y,z],[2^r,2.3^r,3.4^r],[2(2^n-1),3.(3^n-1),4.(4^n-1)]| find the value of sumDelta_r

If Delta_(r) = |(2^(r -1),((r +1)!)/((1 + 1//r)),2r),(a,b,c),(2^(n) -1,(n +1)! -1,n(n +1))| , then sum_(r =1)^(n) Delta_(r) is equal to

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 Delta_(r) = |(1,r,2^(r)),(2,n,n^(2)),(n,(n(n+1))/(2),2^(n+1))| , then the value of sum_(r=1)^(n) Delta_(r) is

If sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

If |(alpha^(2n),alpha^(2n+2),alpha^(2n+4)),(beta^(2n),beta^(2n+2),beta^(2n+4)),(gamma^(2n),gamma^(2n+2),gamma^(2n+4))|=((1)/(beta^(2))-(1)/(alpha^(2)))((1)/(gamma^(2))-(1)/(beta^(2)))((1)/(alpha^(2))-(1)/(gamma^(2))) {where alpha^(2), beta^(2) and gamma^(2) are al distinct}, then the value of n is equal to

If alpha,beta,gamma,delta in R satisfy ((alpha+1)^2+(beta+1)^2+(gamma+1)^2+(delta+1)^2)/(alpha+beta+gamma+delta) = 4 If biquadratic equation a_0 x^4 + a_1 x^3 + a_2 x^2 + a_3 x _ a_4 =0 has the roots (alpha+1/beta -1),(beta +1/gamma -1),(gamma+1/delta -1),(delta+1/alpha -1) . then the value of a_2/a_0 is

If ""^(n)C_(r -1) = 36, ""^(n)C_(r) = 84 " and " ""^(n)C_(r +1) = 126 , then find the value of ""^(r)C_(2) .