Notes - Analysis III TT23, Power series
Flashcards
- Same result as in [[Notes - Analysis III TT23, Power series]]U, [[Notes - Analysis II HT23, Differentiation theorem]]U, but where the proof is actually on the syllabus now.
Proofs
Suppose the power series $\sum _ {k=0}^\infty c _ k x^k$ has radius of convergence $R \in [0, \infty]$. Prove that the radius of convergence of $\sum _ {k = 1}^\infty kc _ k x^{k-1}$ is also $R$.
Todo.