作者arbuztw (Robguns)
看板NTU-Exam
標題[試題] 102下 林楨芸 微積分甲下 第二次小考
時間Thu Jun 26 14:31:02 2014
課程名稱︰微積分甲下
課程性質︰必修
課程教師︰林楨芸
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰
考試時限（分鐘）：50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
QUIZ 2-11.5-11.9
1. Determine whether the following series are convergent.
∞
(a) Σ n^p p^n (p denotes a positive, fixed number)
n=1
∞ 1
(b) Σ -----------. (10 points)
n=2 n^(3/2)-n
∞ (-1)^n (x-1)^3n
2. Given Σ -------------------, find (a) the radius of convergence (b) the
n=1 √(2n+1)
interval of convergence (c) the value(s) of x for which the series conver-
ges conditionally. (10 points)
3
3. Express f(x) = ---------- as the sum of power series by using partial frac-
x^2-3x+2
tions. Find the interval of convergence. (10 points)
x-arctan(x)
4. Evaluate ∫ ------------- dx as a power series. What is the radius of conv-
x
ergence? (10 points)
∞ 1
5. (Bonus) Determine whether the series Σ (-1)^n ln(1+arctan(---)) is
n=1 n
absolutely convergent, conditionally convergent, or divergent. (5 points)
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