This preview shows pages 1–6. Sign up to view the full content.
Math 1432
Register for Test 3
No Class Monday – Work the review posted as blank slides then
check your work using the “lecture” notes.
THINK:
The same three letter word can be inserted
into each of these words to give a longer word in each case.
REED
OUTS
BRICKING
PING
FED
MISS
DEED
BEING
SING
SPED
What is the word?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Notes for series “growth”:
Let p(k) be a polynomial in k.
r
k
for r > 1 grows much faster than p(k)
k! grows much faster than r
k
, p(k)
k
k
grows much faster than the others
Hence,
( 29
( 29
( 29
k
k
k
k
k
k
p k
p k
p k
k
r
k
r
r
k
k
k
k
,
,
!
!
,
,
!
∑
∑
∑
∑
∑
∑
ALL converge rapidly.
Section 11.7
Power Series
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Suppose that
( 29
=

6
x
1 x
f
.
If you divide 1 – x into 6, you get a “polynomial” that continues
forever.
( 29
=
+
+
+
+
+
2
3
4
P x
6 6x 6x
6x
6x
...
This result is a power series.
The word series indicates that there is an infinite number of terms.
The word power tells us that each term contains a power of x.
The series is also a geometric series, with r=x, so the series will
converge for x<1.
By comparing the graphs of
( 29
=

6
x
1 x
f
and P(x) with more and
more terms, you will see that between

1 and 1 (the interval of
convergence), the two graphs converge.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/06/2011 for the course MATH 1432 taught by Professor Morgan during the Spring '08 term at University of Houston.
 Spring '08
 morgan
 Math

Click to edit the document details