Find the sum of the following geometric series :

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

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

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

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

(x – y) S_{n =} (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)S_n

Hence,