1) (a) Determine if the following statements are true or false. If true give a reason...
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1) (a) Determine if the following statements are true or false. If true give a reason or cite a theorem and if false, give a counterexample i) If {a} is bounded, then it converges. ii) If {a} is not bounded, then it diverges. iii) If {an} diverges, then it is not bounded. (b) Give an example of divergent sequences {a} and {b} such that {a, + b} converges. 1) (a) Determine if the following statements are true or false. If true give a reason or cite a theorem and if false, give a counterexample i) If {a} is bounded, then it converges. ii) If {a} is not bounded, then it diverges. iii) If {an} diverges, then it is not bounded. (b) Give an example of divergent sequences {a} and {b} such that {a, + b} converges.
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