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# Generalization of x^n + 1/x^n = k

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Given $x + \frac{1}{x} = k,$ find a formula with $k$ for $x^n + \frac{1}{x}^n$

Nov 14, 2021

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I am not sure what kind of answer you are looking for

I expanded    $$(x+\frac{1}{x})^n$$

and got

$$x^n+\frac{1}{x^n}=k^n-\displaystyle \sum_{r=1}^{n-1}\binom{n}{r} x^{n-2r}$$

Nov 14, 2021