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Let Δ_r denote the determinant [2r-1, {^mC_r}, 1; m²-1, 2^m, m+1; sin²(m²), sin²(m), sin²(m+1)]. Then the value of ∑_(r=0)^(m) Δ_r is

1. 0
2. 4
3. 3
4. 1

Correct answer: 0

Solution

The determinant Delta_r is structured such that its rows exhibit linear dependencies when summed over the range of r from 0 to m, leading to a total sum of zero. This is due to the properties of determinants where linear combinations of rows can result in a determinant of zero.

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