Hi, 1. The problem statement, all variables and given/known data I am asked to prove that if the power series Ʃ(1,infinity) a_n(x-x0)^n converges at a point d, then it converges for every x that satisfies |x-x0|<|d-x0|. 2. Relevant equations 3. The attempt at a solution Obviously |d-x0|<r, where r denotes the radius of convergence. Should I strive to demonstrate that every such x would also satisfy |x-x0|<r? Is that the way to go about proving the above proposition? There is a general rule that if a power series converges at a point a, then it converges at every point x satisfying |x|<|a|. Should I therefore strive to show that |x|<|d|, or am I actually requested to prove the general rule? I'd appreciate some guidance.