Answer :

Let Sn = (x + y) + (x2 + xy + y2) + (x3 + x2 y + xy2 + y3) + …. to n terms


Multiplying and dividing by (x – y) we get,



(x – y) Sn = (x2 – y2) + x3 + x2y + xy2 – x2y – xy2 – y3..upto n terms


(x – y) Sn = (x2 + x3 + x4+…n terms) – (y2 + y3 + y4 +…n terms)


We know that,


Sum of GP for n terms =


We have two G.Ps in above sum, so,


(x – y)Sn


Hence,


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