# Negative Forever

Algebra Level pending

Let $$c$$ be a real number. The sequence $$a_1, a_2, a_3, ...$$ is defined by $$a_1 = c$$ and $$a_n= 2 a_{n-1}^2 -1$$ for all $$n \geq 2$$. Find the sum of $$c$$ such that $$a_n < 0$$ for all $$n \geq 1.$$

This problem is not original.

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