Prove or give a counterexample to the following statement If

Prove or give a counterexample to the following statement: If the sequence (|a_n|) converges to 0, then the sequence(a_n) converges to 0.

Solution

True.

{|an|} converges to 0

So for any e>0 there exists N so that for all n>N

||an||=|an|<e

HEnce, for all e>0 there exists N so thatt for all n>N

|an|<e

So {an} converges to 0