Question 2
a) Let real numbers $a,b,c$ satisfy $a^2+b^2+c^2=1$. Prove
$$|a-b|+|b-c|+|c-a|\le2\sqrt2.$$
b) Let real numbers $a_1,\ldots,a_{2019}$ satisfy $\sum_{i=1}^{2019}a_i^2=1$. Find the largest value of
$$S=|a_1-a_2|+|a_2-a_3|+\cdots+|a_{2018}-a_{2019}|+|a_{2019}-a_1|.$$
$$|a-b|+|b-c|+|c-a|\le2\sqrt2.$$
b) Let real numbers $a_1,\ldots,a_{2019}$ satisfy $\sum_{i=1}^{2019}a_i^2=1$. Find the largest value of
$$S=|a_1-a_2|+|a_2-a_3|+\cdots+|a_{2018}-a_{2019}|+|a_{2019}-a_1|.$$