Question 1
An arithmetic progression has 1987 terms, first term $u_1=\pi/1987$ and common difference $d=\pi/3974$. Determine
$$S=\sum\cos(\pm u_1\pm u_2\pm\cdots\pm u_{1987}),$$
where the sum includes every possible independent choice of a plus or minus sign before each term.
$$S=\sum\cos(\pm u_1\pm u_2\pm\cdots\pm u_{1987}),$$
where the sum includes every possible independent choice of a plus or minus sign before each term.