Homework 3: Due Oct 2nd
(1) Rewrite the following series using the Sigma notation.
1
1
(a) 3 + 1 + 27 +
9
1
1
1
1
(b) 1 + 4 + 9 + 16 + 25 +
(1)n
(2) It is known that n=1 n converges. Find
(1)n
(1)n
Homework 5: Due Nov 29th (Thursday)
(1) Evaluate the limits (note i, j, and k are the three basis vectors in R3 ):
(a) lim (t2 , 4t, 1/t)
t3
(b) lim (e2t i + ln(t + 1)j + 4k).
t0
r(t)
where r(t) = (si
(1) (a) Let
(b) Let
(c) Let
(2) Suppose
Sample midterm 1
an = n n. What is a5 ?
br = 2ar . What is b2 ?
ck = ak ak+1 . Find a formula for ck .
that lim an = 4 and lim bn = 2. Determine
2
n
n
(a) lim a
Sample nal
(1) True or False
(a) There are convergent sequences that are not monotonic.
(b) If lim an = 10 then there is an integer N such that 9.9 < aN < 10.1.
n
(c) There is a sequence an so that a1
Sample midterm 2
(1) The following sequences are convergent. Find their limits.
(a) an = nn+1 .
2
(b) an = n1/n .
(c) a1 = 1, and an+1 = 2 + an for n > 1.
(2) Which of these series converge and why.
n
Homework 5: Due Nov 20th (Tuesday)
x2n
Show that F (x) has innite radius of convergence.
2n n!
n=0
(2) Find the power series for f (x) = x log(1 + x ).
2
1
(3) Find the rst three terms of the Taylor s
Homework 5: Due Nov 1st (Thursday)
(1) Find the radius of convergence for
xn
.
2n
n=0
(2) Find the radius of convergence for
x2n
.
n!
n=0
nxn1 .
(3) Find the closed form for the function
n=0
(4) Find
Homework 4: Due Oct 18th (Thursday)
(1) Find the sum of the series i=1 i1 correct to 3 decimal places.
5
1
(2) How many terms of the series n=1 n log(n)2 would you need to add to fnd
its sum to within
Homework 2: Due Sept 25th
n
(1) Let b1 = 1 and bn+1 = b2 + b1 for all n > 1. Assuming that (bn ) is a
n
convergent sequence, nd its limit.
(2) Let an = (2n + 3n )1/n . Prove that
3 an 21/n 3
for all p
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Homework 1: Due Sept 18th
What is a5 for the sequence an = n2 n?
Let a1 = 1 and an = 1 + a1 + a2 + + an1 for n > 1. Calculate the rst
four terms of the sequence (an ).
Homework 4: Due Oct 9th
(1) Which of the following series converge and why?
n1
(a)
n=1 n n
(b)
n=1
n=1
n=1
n=1
n=1
5n
6n +n
(sin n)2
n4 +n
n
en
1
(n!)2
1
sin n
(c)
(d)
(e)
(f)
(2) Using the integral t
Homework 5: Due Oct 25th (Thursday)
(1) Show that the following series convergent. How many terms of the series
do we need to add in order to nd the sum to the indicated accuracy?
(1)n
(a)
( error le
DEPARTMENT OF ECONOMICS
ECON 2750A
Assignment #2
Prof. K.C. Tran
Due Date:
Thursday, February 8, 2018
1. (a) If the dimension of matrix A is 3 5 and the product AB is 3 7 , what is the
dimension of ma