Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems A First Course in Complex Analysis · Problem 7.5.33
Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka
Mathematics — Complex Analysis · radius-of-convergence
Problem Find the radius of convergence for each of the following series.
(a) ∑ k ≥ 0 a k 2 z k \displaystyle\sum_{k\geq 0} a^{k^2} z^k k ≥ 0 ∑ a k 2 z k a ∈ C a \in \mathbb{C} a ∈ C ∑ k ≥ 0 k n z k \displaystyle\sum_{k\geq 0} k^n z^k k ≥ 0 ∑ k n z k n ∈ Z n \in \mathbb{Z} n ∈ Z ∑ k ≥ 0 z k ! \displaystyle\sum_{k\geq 0} z^{k!} k ≥ 0 ∑ z k ! ∑ k ≥ 1 ( − 1 ) k k z k ( k + 1 ) \displaystyle\sum_{k\geq 1} \frac{(-1)^k}{k} z^{k(k+1)} k ≥ 1 ∑ k ( − 1 ) k z k ( k + 1 ) ∑ k ≥ 1 z k k k \displaystyle\sum_{k\geq 1} \frac{z^k}{k^k} k ≥ 1 ∑ k k z k ∑ k ≥ 0 cos ( k ) z k \displaystyle\sum_{k\geq 0} \cos(k) z^k k ≥ 0 ∑ cos ( k ) z k ∑ k ≥ 0 4 k ( z − 2 ) k \displaystyle\sum_{k\geq 0} 4^k (z-2)^k k ≥ 0 ∑ 4 k ( z − 2 ) k Browse the problem library