I'm trying to find how this series is continuous by proving its infinitely differentiable. In my books, i came across the internal of convergence and the radius of convergence which should help me figure this out, but I cant seem to wrap my head around the concept of the power series to begin with, and my research generally associates this series with the taylor series; is it the same thing? can i still prove that this function is continuous everywhere through this method?
2026-03-25 03:02:57.1774407777
What is the power series of $a^x$
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Hint
$$a^x=e^{x\ln(a)},\quad a>0.$$