21. Simplify the expression

$-1-(-1-(-1-(-1-(\ldots$, if the expression contains:
a) 1989 ones; b) 1990 ones.
21. Observing

$$
\begin{aligned}
& -1-(-1)=-1+1=0 \\
& -1-(-1-(-1))=-1 ; \\
& -1-(-1-(-1-(-1)))=0 ; \\
& -1-(-1-(-1-(-1-(-1))))=-1
\end{aligned}
$$

we notice that with an even number of ones, the result is 0, and with an odd number of ones, the result is -1. Therefore, in case a) we have -1, and in case b) we have 0. [^0]