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