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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
 #1
avatar+115391 
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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

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