Why radius and interval of convergence are important what they tell about the series

Any doubt then you can ask

For example Radius of convergence is 2 and center of your power series is 0, then power series converges for (-2,2)

Yes , These are important concept in Power series as Radius of convergence tells you about on which point this power series converges.

go through this link , it may help you https://youtu.be/wOURocjlq14

pdf will help you

the radius of convergence of a power series is the radius of the largest disk in which the series converges. It is either a non-negative real number or infinity. When it is positiv...