A First Course in Complex Analysis · Problem 7.5.27

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · radius-of-convergence

Problem

(a) Suppose that the sequence (ck)(c_k) is bounded. Show that the radius of convergence of ∑k≥0ck(z−z0)k\sum_{k\geq 0} c_k(z-z_0)^k is at least 11. (b) Suppose that the sequence (ck)(c_k) does not converge to 00. Show that the radius of convergence of ∑k≥0ck(z−z0)k\sum_{k\geq 0} c_k(z-z_0)^k is at most 11.

Related theory

Browse the problem library