作者PttFund (批踢踢基金)
看板Math
标题[分析] 初微(12)
时间Fri Jul 15 01:32:56 2005
Let {a_n} and {x_n} be two real sequences. If a_n > 0 for all n,
1
lim ----------------- = 0,
n→∞ a_1 + ... + a_n
and x_n → x as n → ∞. Show that
a_1 x_1 + ... + a_n x_n
lim ------------------------- = x.
n→∞ a_1 + ... + a_n
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