# a counterexample

1. (a) Prove that if = ¥ then = 0

(b) Give a counterexample to show that the converse (if = 0 then

= ¥) is false.

2. Give an example of a sequence {an} satisfying all of the following:

{an} is monotonic

0 < an < 1 for all n and no two terms are equal

=

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#### Solution Preview

1. (a) Prove that if = ¥ then = 0

Proof: Suppose Let be given. Then there exists a positive integer such that Since there exists a positive ...

#### Solution Summary

A counterexample is exemplified.

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