作者arbuztw (Robguns)
看板NTU-Exam
標題[試題] 102下 林楨芸 微積分甲下 第一次小考
時間Thu Jun 26 14:20:03 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 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
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 123.193.74.170
※ 文章網址: http://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1403763606.A.6BF.html