MathDB

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

\cos 1,\cos 2,\dots,\cos n^2.

(For example, d_3 \equal{} \begin{vmatrix}\cos 1 & \cos2 & \cos3 \\ \cos4 & \cos5 & \cos 6 \\ \cos7 & \cos8 & \cos 9\end{vmatrix}. The argument of

\cos

is always in radians, not degrees.) Evaluate

\lim_{n\to\infty}d_n.

Problem Statement