Browse · MATH Print → jmc algebra senior Problem A sequence is defined by a0=21 and an=1+(an−1−1)2. Compute a0a1a2⋯. Solution — click to reveal Let bn=an−1. Then bn=bn−12, and a0a1a2⋯=(1+b0)(1+b02)(1+b04)⋯=1−b01−b02⋅1−b021−b04⋅1−b041−b08⋯=1−b01=1−(−1/2)1=32. Final answer \frac{2}{3} ← Previous problem Next problem →