Question

According to the theorem of convergence of the power series for what possible values of x can the series converge?:

Answer 1

\[\sum_{n=0}^{\infty} a_{n}x^{n}\]

Answer 2

For every power series, there is a number R
\[
0\le R \le \infty
\]
called the radius of convergence of the series.
For
\[|x| < R
\]
the power series converges absolutely. For |x| = R, the situation must be examined separately.