Question 42
Let $a_1, a_2, \dots, a_n$ be a sequence of real numbers lying between $1$ and $-1$, i.e. $-1 \lt a_i \lt 1$, for $1 \le i \le n$, and such that
(i) $a_1 + a_2 + \dots + a_n = 0$;
(ii) $a_1^2 + a_2^2 + \dots + a_n^2 = 40$.
Determine the smallest possible value of $n$.
(i) $a_1 + a_2 + \dots + a_n = 0$;
(ii) $a_1^2 + a_2^2 + \dots + a_n^2 = 40$.
Determine the smallest possible value of $n$.