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## Homework Statement

Is the proposition

[itex]\sum^{\infty}_{n=1}[/itex]|x[itex]_{n}[/itex]|=0 ⇔[itex]\forall[/itex]n[itex]\in[/itex]IN x[itex]_{n}[/itex]=0

true? If it is true how can we prove that ?

## Homework Equations

## The Attempt at a Solution

I proved the [itex]\Leftarrow[/itex] side of proposition but i could not prove the [itex]\Rightarrow[/itex] side of proposition.