# Dedicated to my best friend

Algebra Level 5

For all $$x \in \mathbb C$$, let $$S_n=x^n+\frac 1 {x^n}$$.

After removing a number $$S_b$$ from the series $$(S_1+S_2+\ldots+S_a)$$ when Sandeep Bhardwaj, the magician, divides the remaining part with $$S_b,$$ he somehow always manages to get another series $$(S_1+S_2+\ldots+S_c)$$ as the answer. Now find the value of $$(a-b-c)$$ and therefore, decipher his trick.

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