Let `S_1,S_2,...,S_101` be consecutive terms of an AP. If `1/(S_1S_2)+1/(S_2S_3)+...+1/(S_100 S_101)=1/6 and S_1S_101=50,` then `|S-S_101|` is equal to

Let S_(1),S_(2),...,S_(101) be consecutive terms of an AP.If (1)/(S_(1)S_(2))+(1)/(S_(2)S_(3))+...+(1)/(S_(100)S_(101))=(1)/(6) and S_(1)S_(101)=50 then |S-S_(101)| is equal to

Let S_(1), S_(2), ...... S_(101) be consecutive terms of A.P. If 1/(S_(1)S_(2)) + 1/(S_(2)S_(3)) + ...... + 1/(S_(100)S_(101)) = 1/6 and S_(1) + S_(101) = 50 , then |S_(1) - S_(101)| is equal to

Let S_(1), S_(2),…, S_(101) be consecutive terms of an AP. If (1)/(S_(1)S_(2)) + (1)/(S_(2)S_(3)) +...+ (1)/(S_(100)S_(101)) = (1)/(6) and S_(1) + S_(101) = 50 , then |S_(1) - S_(101)| is equal to a)10 b)20 c)30 d)40

If S_1,S_2,S_3 be the sum of n, 2n, 3n terms of a G.P., show that : S_1(S_3-S_2)= (S_2-S_1)^2 .

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+4) - 4S_(n+3) + 6S_(n+2) -4S_(n+1) +S_(n) = 0

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

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

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

If S_(1), S_(2) , and S_(3) are, respectively, the sum of n, 2n and 3n terms of a G.P., then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1)^(2)) is equal to

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)