Isn't 100000 such a huge number (Part 11 ) ?

Algebra Level 3

Let \(T(x)=x^{124}+x^{123}+x^{122}+\ldots+x+1\) and \(a_{1},a_{2},a_{3}, \ldots, a_{123},a_{124}\) be the values of \(x\) for which \(T(x) = 0\).

If \(V_{n} = a_{1}^{n} + a_{2}^{n} + a_{3}^{n} + \ldots + a_{124}^{n}\), then find

\[\large \sum_{n=0}^{100000} (-1)^{n}V_{n}\]

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