作者SMer (奈落之夜‧宵)
看板trans_math
标题Re: [数列] 一题证明
时间Wed Sep 6 23:20:04 2006
※ 引述《pobm (待从头收拾旧河山)》之铭言：
: 用定义证明: 如果lim x = a 则对任意自然数k 有lim x = a
: n→∞ n n→∞ n+k
: 谢谢^^
for any e > 0, there is N > 0 such that
|x_n - a| < e whenever n > N
thus |x_(n+k) - a| < e whenever n > N and for all integer k > 0
hence x_(n+k) -> a as n -> oo
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