課程名稱︰微積分
課程性質︰必修
課程教師︰蔡炅男
開課學院：工學院
開課系所︰很多
考試日期（年月日）︰2010-03-10
考試時限（分鐘）：50
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
You should include in your answer every piece of computations and reasonings
so that corresponding partial credit could be gained.
1.Determine whether the following sequence converges or diverges.
If it converges , find the limit.
An=ln|2n^2+1| -ln|n^2+1|
2.A sequence An is given by A1 =√2, A(n+1)=√(2+An)
(a)By induction or otherwise, show {An} is increasing , and bounded by 3.
(b)Why do results in (a) imply An converges?
(c)Find limit An.
3.Find the value c such that
∞
Σ(1+c)^(-n)=2
n=2
4.Determine whether the series is convergent or divergent
∞
Σ 1/(n^2+4)
n=1
5.Determine whether the series is convergent or divergent
∞
Σ(n+2)^0.5/(2n^2+n+1)
n=1
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存在即是合理...
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