If `S_1,S_2,S_3` are the sums of first n natural numbers, their squares and their cubes respectively then `S_3(1+8S_1)=`

If S_(1), S_(2) and S_(3) are the sums of first n natureal numbers, their squares and their cubes respectively, then (S_(1)^(4)S_(2)^(2)-S_(2)^(2)S_(3)^(2))/(S_(1)^(2) +S_(2)^(2))=

If S_1, S_2, S_3 are the sums of first n natural numbers, their squares and cubes respectively, show that 9S_2^ 2=S_3(1+8S_1)dot

If quad S_(1),S_(2),S_(3) are the sum of first n natural numbers,their squares and their cubes,respectively,show that 9S_(2)^(2)=S_(3)(1+8S_(1))

The parabolas y^(2)=4x and x^(2)=4y divide the square region bounded by the lines x=4,y=4 and the coordinate axes.If S_(1),S_(2),S_(3) are the areas of these parts numbered from top to bottom,respectively, then S_(1):S_(2)-=1:1(b)S_(2):S_(3)-=1:2S_(1):S_(3)-=1:1(d)S_(1):(S_(1)+S_(2))=1:2

If S_(1), S_(2), S_(3) are the sums of n, 2n, 3n terms respectively of an A.P., then S_(3)//(S_(2) - S_(1))-