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 \(a\).
by
Calvin Lin