I'm trying to learn how to build the generic series definition for a series of numbers. For some reason I'm having a hard time pulling out this pattern. I'm always pulling out the wrong details for when it comes to building the generic series definition. Is there a more controlled and efficient approach to determining these patterns.
What does it mean when a geometric series can be infinite or finite? It seems to me that you can only find the sum of a series that are finite or when r < |1|. However, I'm understanding that I can use the Maclaurin Series expansion formula to solve for f(x) when x is within range.
I'm just not understanding the application or idea of finding the sum vs. solving for f(x). Are these the same approaches? Am I doing the same thing but deriving a formula to calculate sums for infinite series?
Can someone elaborate on this as I'm having quite the time understanding how to approach these applications.