Talk:Abel's Test for Uniform Convergence

unsure of a step of proof

In the proof,

let

$\bigsize{a_{n+1}-a_n}+\dots+\bigsize{a_{n+k}-a_{n+k-1}}\leq \epsilon$ for all $z \in K$,

I'm unsure of this. Can the convergence and boundedness of the sum guarantee the existence of $\epsilon$?--Hbghlyj (talk) 14:18, 13 March 2024 (UTC)

omission of (z)

Hope the reader will know $a_n$ actually means $\map{a_n}z$. It makes the notation less clumsy. --Hbghlyj (talk) 14:18, 13 March 2024 (UTC)