I'm trying to find the interval of convergence:
I still don't know how to find its interval of convergence. Could you explain the process to me? I really want to understand this concept before my final test on Monday. Thank you.
It is telling us that we need to know when
So we know that the series converges for the above values of x. Note that the test fails when L=1 so we have to check the endpoints on an individual basis. That means we need to plug x=0 and x=2 back into the series and analyze what happens.
I will do one of them and leave the other for you.
when x=0 we get
This series diverges by the integral test, or you can note that it is the tail end of the harmonic series.
You will need to check the other one.
I hope this helps. Good luck