\[\sum_{i=1}^{500}\frac{1}{O_{i}+x_{i}}\]

Where \(O_{i}\) denotes \(i^{th}\) odd number , for a polynomial mentioned below ,

\[x^{500}-2x^{498}+x^{496}-\cdots+x^2-1723\] which has roots , \(x_{1},x_{2},\cdots,x_{500}\)

Evaluate the above summation.

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## Comments

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TopNewestChinmay, if you want an unique answer, we need the expression to be somewhat-symetric. Otherwise we would probably have to use numerical methods.

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You mean , the polunomial should be symetric ? and why won't we get an unique answet ?

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the expression, the summation you gave

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@Aareyan Manzoor .

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@Aareyan Manzoor can you suggest any symmetric format ?

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