Mr. Integral
Math notes/Calculus II/Power Series and Taylor Approximation

Power Series and Endpoint Tests — Cheat sheet

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Core rule

Find RR from ∣x−c∣<R|x-c|<R, then substitute x=c−Rx=c-R and x=c+Rx=c+R into the original series.

Watch for

The radius does not determine endpoint inclusion. At R=∞R=\infty there are no finite endpoints to test.