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Sum it up to 1729

Algebra Level 4

If $V_{n}=a^{n}+b^{n},$ where $a$ and $b$ are the roots of $x^{2}+x+1,$ what is the value of

$\sum_{n=0}^{1729} (-1)^{n} \cdot \ V_{n} ?$

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by Shubhendra Singh

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