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Find value of (x+(1)/(x))^(3)+(x^(2)+(1)...

Find value of `(x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3)`.

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`(x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3)=sum_(n=1)^(n)(x^(n)+(1)/(x^(n)))^(3)`
`=sum_(n=1)^(n)(x^(3n)+(1)/(x^(3n))+3(x^(n)+(1)/(x^(n))))`
`=sum_(n=1)^(n)x^(3n)+sum_(n=1)^(n)(1)/(x^(3n))+3sum_(n=1)^(n)x^(n)+3sum_(n=1)^(n)(1)/(x^(n))`
`=(x^(3)(1-x^(3n)))/((1-x^(3)))+((1-x^(3n)))/(x^(3n)(1-x^(3)))+(3x(1-x^(n)))/((1-x))+(3(1-x^(n)))/(x^(n)(1-x))`.
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