課程名稱︰微積分甲下
課程性質︰大一共同必修
課程教師︰薛克民
開課學院：生農學院,理學院,管理學院
開課系所︰生機系,生工系,工管系(科管組),地質系等
考試日期（年月日）︰2009/3/23
考試時限（分鐘）：40 min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
∞
1.Determine whether the series Σ 1/n^(1+1/n) converges or diverges.
n=1
(10 points)
2.The terms of a series are defined recursively by the equations
5n+1
a1=2, an+1= ── an .
4n+3
Determine whether Σ an converges or diverges.
(10 points)
∞
3.Find the value p for which the series Σ 1/[n(ln n)^p] is convergent.
n=2
(10 points)
∞
4.Test the series Σ [(-1)^n]n/ln n for convergence or divergence.
n=2
(10 points)
5.Find the radius of convergence and interval of convergence of the series
∞
Σ n!(2x-1)^n.
n=1
(10 points)
6.Find the power series representation of f(x)=ln(5-x) and determine the
radius of convergence.
(10 points)
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