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## Homework Statement

Give an example to show that the modulus rule cannot be reversed. Hence give an example of a divergent sequence ([itex]a_{n}[/itex]) such that (|[itex]a_{n}[/itex]|) is convergent.

## Homework Equations

The modulus rule is;

"Let [itex]a_{n}[/itex] be a convergent sequence.

(|[itex]a_{n}[/itex]|) is convergent, then

lim|[itex]a_{n}[/itex]| = |lim[itex]a_{n}[/itex]|"

n is an element of the natural numbers of course, and the limit is the limit as n tends to infinity.

## The Attempt at a Solution

I don't understand what it means by "reverse" of this rule. I assumed originally that it meant give an example of a divergent sequence that wouldn't work, but the "hence" bit afterwards would suggest I have to do the same thing twice, which I'm guessing isn't right. I also have another "show the reverse doesn't work for this rule" question before it, but I'm not entirely sure what is meant by reverse.

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