5. Determine if the statement is true or false. If true. provide an explanation. If false. provide a counter example. (a) If 22:1 an and 22:1 bu both converge. then 22:1 ((1n + bu) converges. I 'x u b It 271:1 an converges. then Inn on = 0. n'x . - 3C c It 11m an : 0. then Zn_1 an converges. n+oc _ I l l d) If 27:1 an 2 L1 and 22:1 on 2 L2. then 22:1(anbn) = LlLQ. ) l e Suppose an > 0 for all n. Then 2:321 an converges if and only if 2:321 a diverges. { ( { (