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Let S(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^...

Let `S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n`, then

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