MA 17, Section 5
November 11, 2004
True or False?
1. If 0 an bn and
2. If
an 6n converges,
bn diverges, then
an diverges.
an 2n converges.
3. Let sn be the n-th partial sum of the series
an . If lim sn = 3, then lim an = 0.
n
n
4. If an > 0 and lim (an+1
MA 17, Section 5
November 11, 2004
Innite Series: Things You Should Know
Infinite Series
1. What is the dierence between a sequence and a series?
2. What does it mean to say that
an = s ?
Two Examples
3. p-series
1
np
converges when p . . . . . . . . . an
MA 17, Section 5
November 11, 2004
Review
Please do not make any assumptions about the composition of the exam
from this set of review problems. Do not assume that the exam questions
will be exactly as the questions below, or slight modications of them. T
MA 17, Section 5
REVIEW
Please do not make any assumptions about the composition of the midterm from this set
of review problems. Do not assume that the exam questions will be exactly as the questions
below, or slight modications of them. The test problem
MATH 17 REVIEW SOLUTIONS, FALL 2004
MICHAEL LAUZON
1. Differential Equations
1.1. First order equations. Solve for the General solution and then the solution
that ts the given initial data, if given.
dy
= y 2 , y (0) = 1
(1 + x2 )
dx
Answer: y = tan11(x)+
MATH 17 REVIEW, FALL 2004
MICHAEL LAUZON
1. Differential Equations
The important things to remember from dierential equations is how
to solve for solutions of rst order linear, rst order separable, and
second order linear equations with constant coecients
FINAL EXAM
1. (20 points). Find the orthogonal trajectories of the family of curves
$2 _ y2 : k
and sketch a rough picture of the two families.
-2, J :
27 3;: o
)1 4 2r , 5 f - w
s / V /=' X
y? 2 Z J» MATHEMATICS 17 / BROWN UNIVERSITY / FALL 2004
2.