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We consider a recursively defined sequence and prove the convergence by showing that the sequence is monotone and bounded. a_1 = 0, a_n+1 = 1 - 1(2+a_n) sequence, recursive, recursive, defined, defined, monotone, bounded, convergence, converges, method, limit, limit, determine, calculate, determination, induction, complete, complete, estimate, estimate, example, task, exercise, solution, exam, test, analysis, show, demonstrate, proof, prove, sequence convergence, calculate, calculate