作者arbuztw (Robguns)
看板NTU-Exam
标题[试题] 102下 林桢芸 微积分甲下 第一次小考
时间Thu Jun 26 14:20:03 2014
课程名称︰微积分甲下
课程性质︰必修
课程教师︰林桢芸
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰
考试时限（分钟）：50
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
QUIZ 1-11.1-11.4
∞ 1
1. Find the values of p for which the series Σ ------------ is convergent.
n=3 n^p(ln n)^2
∞ 1 1
Suppose p≧0, determine whether Σ sin(-----) ---------- is convergent.
n=3 n^p (ln n)^2
(15 points)
1
2. Determine whether the following sequences converge: (a) lim n ln(1+---)
n→∞ n
and (b) lim n (p^(1/n) - 1) where p >0 is some fixed constant. (10 points)
n→∞
_ ____ _______
3. Show that sequence { √2, √2√2, √2√2√2, ... } converges and find the
limit. (10 points)
∞ 1
4. Determine whether Σ ------------- converges. (10 points)
n=0 n ln(1+1/n)
∞ cos^n(x)
5. Find the values of for which the series Σ ---------- converges. Find the
n=1 2^n
sum of the series for those values of x. (5 points)
6. (Bonus problem) Find the values of p for which the series
∞ ___ _ ___
Σ n^p (√n+1 - 2√n + √n-1) converges. (5 points)
n=1
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