# If S1,S2and S3 are the sum of first n, 2n and 3n terms of a geometric series respectively,then prove that S1(S3 – S2) = (S2 – S1)2.

Sum of n terms =

S1 =

S2 =

S3 =

Putting value of S1, S2 and S3 on the left side, we get:

S1(S3 – S2) =

S1(S3 – S2) =

S1(S3 – S2) =

S1(S3 – S2) =

S1(S3 – S2) = ………..(1)

Now, we solve the right side by putting S1, S2 and S3 :
(S2– S1)2 =

(S2– S1)2 = ………….(2)

From (1) and (2), we have:

Left hand side = Right Hand side

Hence Proved.

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