Inspired by Loomba and Hung Woei

Algebra Level 4

\[ { \begin{cases} a+a^2+a^3+ a^4 + \cdots= 2 \\ a^2+a^3+a^4+ a^5 + \cdots=1 \\ \end{cases}} \]

Given the above, find \(a\).


Inspiration.

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