Sum the series : `x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3+ ton`terms. – InterviewSolution

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1.	Sum the series : `x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3+ ton`terms.
Answer» `x(x+y)+x^2(x^2+y^2)+....n` terms `=>x^2+xy+x^4+x^2y^2+x^6+x^3y^3+...n` terms `=>(x^2+x^4+x^6+...n ` terms `)` +`(xy+(xy)^2+(xy)^3+...n` terms`)` Now, we have `2` G.P. with first term and common ratio `x^2` and `xy`. Sum of a G.P. can be given as, `S_n = (a(r^n-1))/(r-1)` `:. S_n = (x^2(x^(2n) - 1))/(x^2-1)+(xy(xy^n - 1))/(xy-1)`

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