http://www.lib.nccu.edu.tw/exam/transfer/math/index.htm 这个是政大应数考古题的网址 我要问的是92年微积分(一)的第3,6,7题 题目如下,看不清楚的可以去上面的网址看 3.the series ∞ cos(n^p) ∞ (lnn)^β cos(n^p) Σ ------------ and Σ -------------------- n=2 n(lnn)^α n=2 n^α converge for every α>1,β>=1 and p>=1. 6.the following series is a rearrangement of the alternating harmonic series in which there appear alternately three positive terms followed by two negative terms 1 1 1 1 1 1 1 1 1 1 + --- + --- - --- - --- + --- + --- + ---- - --- - --- +++--... 3 5 2 4 7 9 11 6 8 show that this series converges and has sum ln(√6). 7.for the sequence of functions f_n(x) = (x^2-1)^n. (3) define g_n(x) = f_n (x), n>=1. g_0(x) = 1. then prove or disprove g_n(x) converges uniformly in [0,√2]. --

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