推 eric80520 :謝謝你們 05/23 21:24
※ 引述《eric80520 (freejustice)》之銘言：
: 題目是 ∞
: Suppose that {a } is a bounded sequence of real numbers.
: k k=0
: Prove that ∞
: f(x):= Σ (a *x^k)
: k=0 k
: has a positive radius of convergence.
|a_k x^k|< M |x|^k
hence, Σ|a_k x^k|< M Σ|x|^k
and Σ|x|^k is convergent if |x|<1
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 112.104.114.134
※ 編輯: JohnMash 來自: 112.104.114.134 (05/20 12:58)