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Investigate special cases for small n first.
Can you spot patterns in the sums for n=3, 4, 5, 6, 7 \dots?
In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?