If `D_r=|(1/2^(r-1),1/3^(r-1),1/5^(r-1)), (x,y,z), (2,3/2,5/4)|` then `sum_(r=1)^oo D_r` is

If D_(r)=det[[(1)/(2^(r-1)),(1)/(3^(r-1)),(1)/(5^(r-1))x,y,z2,(3)/(2),(5)/(4)]] then sum_(r=1)^(oo)D_(r) is

If D_(r)=|(2^(r-1),2(3^(r-1)),4(5^(4-1))),(x,y,z),(2^(n)-1,3^(n)-1,5^(n)-1)| then sum_(r=1)^(n)D_(r)=

If D_r=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then prove that sum_(r=1)^n D_r=0.

If D_r=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then prove that sum_(r=1)^n D_r=0.

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 "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 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