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

Algebra Level 4

Let T(x)=x124+x123+x122++x+1T(x)=x^{124}+x^{123}+x^{122}+\ldots+x+1 and a1,a2,a3,,a123,a124a_{1},a_{2},a_{3}, \ldots, a_{123},a_{124} be the values of xx for which T(x)=0T(x) = 0.

If Vn=a1n+a2n+a3n++a124nV_{n} = a_{1}^{n} + a_{2}^{n} + a_{3}^{n} + \ldots + a_{124}^{n}, then find

n=0100000(1)nVn\large \sum_{n=0}^{100000} (-1)^{n}V_{n}

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