THANK YOU
If a power series equals zero, does it converge or diverge?
(I'm trying to figure out if an endpoint should be included in the interval of convergence)
You're welcome! I'd be happy to explain how to determine convergence or divergence of a power series.
To determine if a power series converges or diverges, we can use the convergence tests. However, if the power series equals zero for all values of the variable within a given interval, it converges to zero everywhere within that interval. This is known as the "trivial case" of convergence.
In your case, if you have a power series that equals zero, it will converge regardless of the value of the variable. Thus, the interval of convergence will include the endpoint(s) of the given interval.
Keep in mind that if a power series does not equal zero for at least one value of the variable within its interval of convergence, you would need to apply convergence tests to determine if it converges or diverges.
I hope this explanation helps! Let me know if you have any more questions.