[考古] 政大應數92年微積分(一)
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我要問的是92年微積分(一)的第3,6,7題
題目如下,看不清楚的可以去上面的網址看
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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