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**Barak****Member**- Registered: 2005-11-19
- Posts: 1

Question:

prove that if |a|<0 then

lim n(a^n) = 0

n-> ∞

please give me a hint or an explaination to how to solve this problem.

:-)

Barak

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

Let a ∈ ℝ. Accoding to you condition, |a|<0, we can build the set:

A = {a ∈ ℝ : |a|<0}

From the definition of absolute value, we conclude that A = ∅. So with |a|<0...."there's nothing left to prove". : )

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**zhaobin****Member**- Registered: 2005-11-19
- Posts: 1

I think he mean |a|<1

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

He hasn't complained yet

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