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1) (a) Determine if the following statements are true or false. If true give a reason...

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 n } is bounded, then it converges.

ii) If { a n } is not bounded, then it diverges.

iii) If { a n } diverges, then it is not bounded.

(b) Give an example of divergent sequences { a n } and { b n } such that { a n + b n } converges.

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