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討論串[分析] 均勻收斂
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Verify that the following series is convergent,but not uniformly convergent. in the open interval (0,1). f_n(z) = z + { z(z-1)+z^2(z-1)+z^3(z-1)+.....
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想請問：. if f_n(x) conv. uniformly. a_n*f_n(x) conv. pointwisely. then a_n*f_n(x) conv. uniformly???. --------------------------------------. 目前觀察的結果有：.
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條件只要：. f_n：S→R , f：S→R. 1.f_n is bdd. for all n. 2.f_n → f uniformly. then f is bdd. on S. pf：. Since f_n is bdd. for all n. │f_n(x)│<= M_n , for all
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0 , x=0. lim f_n(x) =. n→inf 1/x , x€(0,inf). (pf：1.x=0： trivial. 2.x€(0,inf)：. nx x. (nx)/(1+nx^2)=─────=─────. 1+nx^2 1 + x^2. ─. n. when n goes to
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