Student number
Name [SURNAME(S), Givenname(s)]
MATH 101, Section 212 (CSP)
Week 10: Marked Homework Assignment
Due: Thu 2011 Mar 24 14:00
HOMEWORK SUBMITTED LATE WILL NOT BE MARKED
1. Determine whether the series is absolutely convergent, conditionally convergent, or
divergent.
(a) 1 −
1
3
+
1
5
1
7
−
+...
(−1)j
j=2 j (ln j)3
(b)
P∞
(c)
P∞
(d)
P∞
(e)
P∞
(f)
P∞
k=0 (−1)
`=0 (−1)
k
` 1002`+1
(2`+1)!
(−1)m−1 10002m−1
m=1 m! (m−1)! 22m−1
n=1 (−1)
n+1 n!
nn
2. What does the Ratio Test say about the convergence or divergence of the p-series
P∞ 1
n=1 np for p > 0?
3. Let
Is


P∞
n/2n if n is a prime number
an = 
1/2n otherwise.
n=1
an convergent? Give reasons for your answer.
4. Find the radius of convergence and interval of convergence of the power series.
(a) x −
(b)
P∞
(c)
P∞
(d)
P∞
(e)
x3
3
+
x5
5
(−1)n
−
x7
7
+...
x2n+1
n=0 n! (n+1)! 22n+1
k=0
k!(x+2)k
106k
(x−2)n
5n
P∞ (x−2)n
n=1 n 5n
n=0
5. Find a power series whose interval of convergence is
(a) (−1, 5)
(b) [−1, 5)
(c) (−1, 5]
(d) [−1, 5]