Math 231 Worksheet #12
1. (Review)
1
a) The series n is called the . . . series. It is convergent/divergent.
n=1
Solution:
Harmonic series. It is divergent.
b) The integral 1 x1p dx is convergent for
Math 231 Worksheet #8 Solutions
1. This problem concerns the curve C dened by
y = 3 3x
y
0x1
(a) Sketch the curve and use geometry to compute its length.
Solution 1a:
From Pythagorean theorem: L2 = 32
Math 231 Worksheet #9 Solution
1. Let cfw_an be a sequence.
(a) What does it mean to write an L?
Solution:
an L means limn an = L. The sequence an has the limit L so for large
values of n, the an are
Math 231 Worksheet #11 Solutions
1. A series has a sum if what sequence has a limit?
Solution:
an = a1 + a2 + . . . + an , let sn denote the nth partial sum
Given a series
n=1
s n = n ai = a1 + a2 + .
Math 231 Worksheet #10 Solutions
1. Recall that the rule of distribution says that for any real numbers
X(C0 + C1 ) = XC0 + XC1
(A + B)Y = AY + BY
(a) By rst letting X = (A + B), show the distribution
Math 231 Worksheet #13 Solutions
1
1. (a) Use the comparison test with n2 to show n21 converges.
n=1
n=1
+1
Solution:
1
n21 for all n 1
n2
+1
1
We know that
n=1 n2 converges by the integral test, so
Math 231 Worksheet #14 Solutions
1. What is the dierence between a series absolutely converging, conditionally converging
and diverging?
Solution:
A series
an is called absolutely convergent if the se
1. (10 points each)
Determine if the series is absolutely convergent, conditionally convergent
or divergent. Be sure to show your reasoning. No work, no credit.
(a)
1
X
n=5
p
1
n3 + 10n
1
X ( 1)n
(b)