[微積] 一題高微

[Helilo (哈里路)]

原題目如下

Let E={rational numbers in [0,1]}={a_n, n belongs to N }.

Let b_n = 2^-n, n=1,2,3,... Function h_x(t) is defined by


h_x(t)=  1,  t<=x
      =  0,  t>x

Function f(t) is defined by

       ∞
f(x)=  Σ b_n*h_x(a_n),  0<=x<=1
       n=1

Prove that f is continuous at every irrational point in [0,1].


想了好一陣子實在不知從何下手
還請各位賜教<(_ _)>

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