If a power series converges for any value x, then R=∞. I don't understand because if a power series converges for any value x doesn't that mean that for any value x the series converges to a finite number? How then is R=∞?

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If a power series converges for any value x, then R=∞. I don't understand because if a power series converges for any value x doesn't that mean that for any value x the series converges to a finite number? How then is R=∞?

OCW Scholar - Single Variable Calculus
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Dont understand your question my friend. Can you try to state that in other words? Hope I can help you!
In this case R might be the radius of convergence. Since the series converges for any real number, x, the radius within which it converges is infinite.
Yeah I was confused the range of convergence and radius of convergence. Thank you both!

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