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PROJ12.PRO
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1989-05-26
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PROJECT 12.
Consider the sequence of determinants
│ 2 -1 │ │ 2 -1 0 │ │ 2 -1 0 0 │
│ -1 2 │ , │ -1 2 -1 │ , │ -1 2 -1 0 │ , etc.,
│ 0 -1 2 │ │ 0 -1 2 -1 │
│ 0 0 -1 2 │
with 2's on the main diagonal, -1's on the sub- and super-diagonals, and 0's elsewhere.
Make a conjecture concerning the numerical value of determinants of this kind.
Try to prove your conjecture.
Can you generalize?