(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that lim[itex]_{n} p_{n}= p[/itex] iff the sequence of real numbers {d{p,p[itex]_{n}[/itex]}} satisfies lim[itex]_{n}[/itex]d(p,p[itex]_{n}[/itex])=0

2. Relevant equations

3. The attempt at a solution

I think I can get the first implication. If [itex]lim_{n} p_{n}[/itex]= p, then we know that d(p,p[itex]_{n}[/itex]) = d(p[itex]_{n}[/itex],p) <[itex] \epsilon[/itex]. Then given [itex]\epsilon[/itex] > 0 and some N, for n>N we have |d{p,p[itex]_{n}[/itex]-0|<d{p,p[itex]_{n} = d(p_{n},p) < \epsilon[/itex].

I'm having a little trouble with the backwards implication, do I just do what I did up above but backwards sorta? Or should I pick some p[itex]_{n}[/itex] and show that it converges to 0, like 1/n or something.

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# Homework Help: Convergence on metric

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