Find the sum of the GP :

x(x + y) + x2(x2 + y2) + x3(x3 + y3) + …. To n terms


The given expression can be written as


= (x2+ xy) + (x4 + x2y2 ) + (x 6 + 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, , when r≠1. ‘Sn’ represents the sum of the G.P. series upto 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


∴


⇒


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