If `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)`.

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 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))=

Let the sum of n, 2n, 3n terms of an A.P. be S_1,S_2 and S_3 , respectively, show that S_3=3(S_2-S_1) .

The parabolas y^2=4xa n dx^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-=1:2 S_1: S_3-=1:1 (d) S_1:(S_1+S_2)=1:2

The parabolas y^2=4xa n dx^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-=1:2 S_1: S_3-=1:1 (d) S_1:(S_1+S_2)=1:2

Let the sum of n, 2n, 3n terms of an A.P. be S_(1), S_(2) and S_(3) respectively. Show that S_(3) = 3(S_(2) - S_(1)) .

If s_(1),s_(2)and s_(3) are the sum of first n , 2n, 3n terms respectively of an arithmetical progression , then show that s_(3)=3 (s_(2)-s_(1))

If the sum of n , 2n , 3n terms of an AP are S_1,S_2,S_3 respectively . Prove that S_3=3(S_2-S_1)

If the sum of n, 2n, 3n terms of an A.P are S_(1), S_(2), S_(3) , respectively, prove that S_(3) = 3 (S_(2) -S_(1)).

If the sum of n, 2n and infinite terms of G.P. are S_(1),S_(2) and S respectively, then prove that S_(1)(S_(1)-S)=S(S_(1)-S_(2)).