推 JohnMash :推 05/20 09:56
※ 編輯: snaredrum 來自: 68.48.173.107 (05/20 11:06)
推 eric80520 :謝謝 05/23 21:17
※ 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.
: 可以幫忙解答嗎?
: 謝謝
a_k is bounded so
a_k < M, for some M which is a positive finite number
so take n^th root as n-->oo should less or equal 1
i.e. radius of convergence is greater or equal than 1
---
感謝Herstein大 指正
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