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in Geometric Progressions by (15.7k points)

Find the sum of the GP : 

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

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1 Answer

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by (15.2k points)

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

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