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Limits

ahmed sobhy
in Analysis and Calculus

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what is the limit of a^n as n reaches infinity if a <-1, and WHY ?

 

I asssume that you are working over the set of real numbers, and that n is a natural number.

 

The sequence that you propose has no limit. In fact the absolute value grows without bound, and the sign oscillates depending on whether n is even or odd.

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