Operations on Power Series
Lets recall somethings we already know. Let
Theorem 1.
c
Let
=
an and
(can )
bn be series of real numbers.
bn be convergent series and c R. Then
an and
an
n=1
1
and
an
n=1
n=1
+
bn
=
n=1
Denition 2. By a rearrangement of
(an +bn
Commonly Used Taylor Series
series 1 1x
when is valid/true
= =
1 + x + x2 + x3 + x4 + . . .
note this is the geometric series. just think of x as r
xn
n=0
x (1, 1)
e
x
=
x x x 1+x+ + + + . 2! 3! 4! xn n! n=0
2
3
4
so: e=1+1+ e
(17x)
1 2!
+
1 3!
+
1 4!
+ .
LHomework on Taylor/Macleurin Polynomials and Series - Part 2 # (5
Do parts (a) - for the following three problems.
(1) at) 2- cos(17a:) so =- 0 J = (00, oo) -= R
(2) no =(1+x)-3 mo .-_ J: (a,
(3) n") = em x0 :3 I? J : (16,19)
You might nd it easier
LI-Iomework on Taylor/Maelaurin Polynomials and Series - Part 2 # (3) 1
Do parts (a) - for the following three problems.
(1) f(33)=(:0$(17&?] ' $9 = 0 J = {00, oo) : R
(2) no = (1 + o3 330 = J = (o,
(3) at) r ex 390 as? l? J = (16,19)
You might nd it e
Math 142
Taylor and Maclaurin Polynominals
Read this handout thoroughly and then
do Homeworks: 2, 4, 5, and 6 (on a seperate sheet of paper).
Lets consider a function
y = f (x)
and x a point x0 in the domain of y = f (x). So the graph of y = f (x) goes th
Even/Odd-ness of Maclaurin Polynominals
set-up
Throughout this handout, there is the set-up (i.e. notation).
The interval I is centered at 0 and of radius R > 0, so I = (R, R). Let
h : I R be any function (naturally, from I into R)
g : I R be any dierenti