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Question Number 68782 by Maclaurin Stickker last updated on 06/Oct/19

Let d_{n} be the determinant of the n \times n

matrix whose entries, from left to right

and then from top to bottom, are

c o s 1, c o s 2, \dots, c o s n^{2} . (For example,

d_{3} = | \begin{matrix} c o s 1 c o s 2 c o s 3 \\ c o s 4 c o s 5 c o s 6 \\ c o s 7 c o s 8 c o s 9 \end{matrix} | .

The argument of c o s is always in radians

not degrees .)

Evalue \lim_{n \to \infty} d_{n .}