[分析]if fn(x)converge pointwise..is f(x) bounded?

[gp3gp3 (gp3gp3)]

原題目如下：

Consider a sequence of functions f (x) (以下用fn(x)表示)
                                  n

,each fn(x) is a bounded function. If fn(x) converges pointwise

to f(x), is it true that f(x) is a bounded function?

If fn(x) converges uniformly to f(x),

is it true that f(x) is a bounded function?  (題目完)


第二個部分（converges uniformly的情形）我有證出來，

然後  我直覺覺得第一個converges pointwise時  答案應該是 不一定

可是又想不到反例＠＠      請教了～ 謝謝！！




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推 math1209    :f_n(x) = 1 + x + ... + x^n. x in (0,1).