The given expression can be written as
= (x2+ xy) + (x4 + x2y2 ) + (x6 + x3y3 ) + …. To n terms
= (x2 + x4 + x6 + … to n terms ) + ( xy + x2y2 + x3y3 + … to n terms )
Sum of a G.P. series is represented by the formula, Sn = a\(\frac{r^n - 1}{r - 1}\) , when r≠1.
‘Sn’ represents the sum of the G.P. series up to nth terms,
‘a’ represents the first term,
‘r’ represents the common ratio and
‘n’ represents the number of terms.
a= x2 first part and xy for the second part
r = (ratio between the n term and n-1 term) x2 for the first part and xy for the second part n terms