作者iddee (好痛哥哥)
看板Math
标题Re: [分析] 初微(6)
时间Mon Jul 11 08:35:07 2005
※ 引述《PttFund (批踢踢基金)》之铭言:
: If
: c_0 + c_1/2 + ... + c_n/(n+1) = 0,
: where c_i is real. Prove that
: c_0 + ... + c_n x^n = 0
: has at least one root between 0 and 1.
n (c_i)x^i+1
By assumption => x=0 and x=1 are roots of Σ -----------
i=0 i + 1
Roll's Thm. => there is x_0 between 0 and 1 s.t.
n
Σ (c_i)(x_0)^i = 0
i=0
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◆ From: 61.219.178.212
※ 编辑: iddee 来自: 61.219.178.212 (07/11 08:37)
1F:→ eggsu :如何由Roll's Thm.推知有解?为何c_0和Σc_i异号? 04/17 00:07
2F:→ eggsu :我看懂了……真是尴尬! 04/17 00:10