If `S_m=(1+2+3+....+m)/m` then `s_1^2+s_2^2+s_3^2+....+s_n^2=`

S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =

If S_(1),S_(2),S_(3),...S_(m) be the sum of first n terms of n A.P. Whose first terms are 1,2,3,... M aand common differnece are 1,3,5,...(2m-1) respectively, show that S_(1)+S_(2)+S_(3)+...+S_(m)= (mn)/(2)(mn+1) .

If S_(1), S_(2), S_(3), …, S_(m) are the sums of n terms of m A.P.'s whose first terms are 1, 2, 4, …, m and whose common differences are 1, 3, 5, …, (2m-1) repectively, then show that S_(1)+S_(2)+S_(3)+…+S_(n)=(1)/(2)mn(mn+1)

If S_(1),S_(2),S_(3),...,S_(m) are the sums of the first n terms of m arithmetic progressions,whose first terms are 1,4,9,16,...,m^(2) and common difference are 1,2,3,4,...,m respectively,then the value of S_(1)+S_(2)+S_(3)+...+S_(m):

If S_1,S_2, S_3, S_m are the sums of n terms of m A.P. ' s whose first terms are 1,2,3,....m and common differences are 1,3,5, ....(2m-1) respectively. Show that S_1+S_2.....+S_m=(m n)/2(m n+1)

If S_1,S_2, S_3, S_m are the sums of n terms of m A.P. ' s whose first terms are 1,2,3, ,m and common differences are 1,3,5, ,(2m-1) respectively. Show that S_1+S_2,+S_m=(m n)/2(m n+1)

If S_1,S_2, S_3, S_m are the sums of n terms of m A.P. ' s whose first terms are 1,2,3, ,m and common differences are 1,3,5, ,(2m-1) respectively. Show that S_1+S_2,+S_m=(m n)/2(m n+1)

If S_1,S_2, S_3, S_m are the sums of n terms of m A.P. ' s whose first terms are 1,2,3,....m and common differences are 1,3,5, ....(2m-1) respectively. Show that S_1+S_2.....+S_m=(m n)/2(m n+1)

If S_1,S_2, S_3, S_m are the sums of n terms of m A.P. ' s whose first terms are 1,2,3,....m and common differences are 1,3,5, ....(2m-1) respectively. Show that S_1+S_2.....+S_m=(m n)/2(m n+1)

If S_1 , S_2 and S_3 are respectively the sum of n, 2n and 3n terms of a G.P., then prove that S_1(S_3 - S_2) = (S_2 - S_1)^2 .