[分析] 初微(12)

[PttFund (批踢踢基金)]

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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