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.