Find the sum of `n` terms of the sequence `(x+1/x)^2,(x^2+1/(x^2))^2,(x^3+1/(x^3))^2, `

Explanation

Let S_n​ denote the sum to n terms of the given sequence.

Then,

`S_n​=(x+1/x​)^2+(x^2+1/x^2​)^2+(x^3+1/x^3​)^2+....+(x^n+1/x^n​)^2`

`=(x^2+1/x^2​+2)+(x^4+1/x^4​+2)+.....+(x^(2n)+1/(x^(2n))​+2)`

`=(x^2+x^4+.....+x^(2n))+(1/x^2+1/x^4​​+.....+1/(x^(2n))​)+n times(2+2+....+n)​`

using,
Sum=`(ar^n-1)/(r-1)`


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