# 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.