※ 引述《pobm (待從頭收拾舊河山)》之銘言：
: 用定義證明: 如果lim x = a 則對任意自然數k 有lim x = a
: n→∞ n n→∞ n+k
: 謝謝^^
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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