Sign in with Facebook
James Stewart’s Followers (51)
James Stewart
Website
![Calculus [With CDROM]](https://i.gr-assets.com/images/S/compressed.photo.goodreads.com/books/1170573179i/61297._SX50_.jpg)
|
Calculus [With CDROM]
—
published
1986
—
78 editions
|
|
|
Calculus: Early Transcendentals
—
published
1995
—
103 editions
|
|
|
Multivariable Calculus
—
published
1991
—
38 editions
|
|
|
Essential Calculus
—
published
2006
—
43 editions
|
|
|
Precalculus: Mathematics for Calculus (with CD-ROM and Ilrn ) [With CDROM]
by
—
published
1997
—
24 editions
|
|
|
Calculus: Concepts and Contexts [With CD-ROM]
—
published
1997
—
42 editions
|
|
|
Single Variable Essential Calculus: Early Transcendentals
—
published
1995
—
41 editions
|
|
|
Single Variable Calculus
|
|
|
Multivariable Calculus: Early Transcendentals
—
published
2002
—
11 editions
|
|
|
Algebra And Trigonometry
by
—
published
2000
—
36 editions
|
|
“You know, I just love Grace Kelly. Not because she was a princess, not because she was an actress, not because she was my friend, but because she was just about the nicest lady I ever met. Grace brought into my life as she brought into yours, a soft, warm light every time I saw her, and every time I saw her was a holiday of its own. No question, I’ll miss her, we’ll all miss her, God bless you, Princess Grace.”
―
―
“Notice that if , then and , whereas if
, then and .
(a) If is absolutely convergent, show that both of the
series and are convergent.
(b) If is conditionally convergent, show that both of the
series and are divergent.
44. Prove that if is a conditionally convergent series and
is any real number, then there is a rearrangement of
whose sum is . [Hints: Use the notation of Exercise 43.
an an
0 a
n
an
0
an an
0 an
0
an
an
an
a
n
an
an
a
n
an
r
an
r
Take just enough positive terms so that their sum is greater
than . Then add just enough negative terms so that the
cumulative sum is less than . Continue in this manner and use
Theorem 11.2.6.]
45. Suppose the series is conditionally convergent.
(a) Prove that the series is divergent.
(b) Conditional convergence of is not enough to determine whether is convergent. Show this by giving an
example of a conditionally convergent series such that
converges and an example where diverges.
r an
r
an
n
2
an
an
nan
nan
nan
an
We now have several ways of testing a series for convergence”
― Calculus: Early Transcendentals
, then and .
(a) If is absolutely convergent, show that both of the
series and are convergent.
(b) If is conditionally convergent, show that both of the
series and are divergent.
44. Prove that if is a conditionally convergent series and
is any real number, then there is a rearrangement of
whose sum is . [Hints: Use the notation of Exercise 43.
an an
0 a
n
an
0
an an
0 an
0
an
an
an
a
n
an
an
a
n
an
r
an
r
Take just enough positive terms so that their sum is greater
than . Then add just enough negative terms so that the
cumulative sum is less than . Continue in this manner and use
Theorem 11.2.6.]
45. Suppose the series is conditionally convergent.
(a) Prove that the series is divergent.
(b) Conditional convergence of is not enough to determine whether is convergent. Show this by giving an
example of a conditionally convergent series such that
converges and an example where diverges.
r an
r
an
n
2
an
an
nan
nan
nan
an
We now have several ways of testing a series for convergence”
― Calculus: Early Transcendentals
Topics Mentioning This Author
| topics | posts | views | last activity | |
|---|---|---|---|---|
| Historical Fictio...: 3 books to take on a deserted island... | 149 | 891 | Jul 03, 2021 10:01PM |
Is this you? Let us know. If not, help out and invite James to Goodreads.
