IMC 1997 Problem 2

Let $a_n$ be a sequence of reals. Suppose $\sum a_n$ converges. Do these sums converge aswell?

(a) $a_1+a_2+(a_4+a_3)+(a_8+...+a_5)+(a_{16}+...+a_9)+...$

(b) ${a_1+a_2+(a_3)+(a_4)+(a_5+a_7)+(a_6+a_8)+(a_9+a_{11}+a_{13}+a_{15})+(a_{10}+a_{12}+a_{14}+a_{16})+(a_{17}+a_{19}+...}$