How does one begin to find an asymptotic function of an infinite power series?

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Say we have the infinite series $$\sum_{n=0}^\infty a_nx^n.$$ We want to attempt to find an asymptotic function/relation to the above series. How does one begin? I have never dealt with this area of math (undergraduate at the moment). Does one need the closed form of the infinite series in order to find the asymptotic behavior?