Convergence is obvious here

Algebra Level 4

\[ \sqrt{1-\sqrt{2-\sqrt{3-\sqrt{4+\sqrt{1-\sqrt{2-\sqrt{3-\sqrt{4+\cdots}}}}}}}} = \ ? \ \]

Details and assumptions:

  1. The sign pattern is \( (---+) \).
  2. The number pattern is \( (1234) \).
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