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

Let {a_{n}} be a sequence with positive terms such that lim a_{n}= L > 0.

Prove lim (a_{n})^{x}= L^{x}.

2. Relevant equations

If x is a real number, there exists an increasing rational sequence {r_{n}} with limit x.

A monotone sequence {a_{n}} is convergent if and only if {a_{n}} is bounded.

a^{x}= lim a^{rn}.

3. The attempt at a solution

I know that each of the individual elements of the sequence {(a_{n})^{x}} converge to (a_{n})^{x}, but I do not know what else I can do from here.

Any help would be greatly appreciated. Thanks!

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# Homework Help: Limit of infinite sequence raised to a real number power

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