Consider the series $sum_{n=1}^infty frac{(-1)^n}{n+x}$
up vote
1
down vote
favorite
Consider the series
$$sum_{n=1}^infty frac{(-1)^n}{n+x}$$
Find all $x in mathbb{R}$ at which the series converges. Converges absolutely. Find all intervals of $mathbb{R}$ where the series defining $f$ converges uniformly, and all intervals of $mathbb{R}$ on which $f$ is continuous
I'm very confused about how to think about this
real-analysis continuity uniform-continuity
edited Nov 16 at 5:24
Eevee Trainer
97311
asked Nov 16 at 5:08
kiarasaini
61
add a comment |
up vote
1
down vote
favorite
Consider the series
$$sum_{n=1}^infty frac{(-1)^n}{n+x}$$
Find all $x in mathbb{R}$ at which the series converges. Converges absolutely. Find all intervals of $mathbb{R}$ where the series defining $f$ converges uniformly, and all intervals of $mathbb{R}$ on which $f$ is continuous
I'm very confused about how to think about this
real-analysis continuity uniform-continuity
edited Nov 16 at 5:24
Eevee Trainer
97311
asked Nov 16 at 5:08
kiarasaini
61
you just need to know the definitions of conditional convergence, absolute convergence, uniform convergence and apply them to your series, it is not so complicate
– Masacroso
Nov 16 at 5:27
Do you know the conditions which guarantee the convergence of an alternating series?
– John Wayland Bales
Nov 16 at 5:28
@JohnWaylandBales it's not quite so simple if I'm not mistaken, at least for $x<0$.
– qbert
Nov 17 at 5:34
@qbert My question was intended to gauge just how confused the OP is. The first two should be easy aside from the negative integers.
– John Wayland Bales
Nov 17 at 6:27
@JohnWaylandBales fair enough and definitely true about the first two and uniform convergence on the nonegatives
– qbert
Nov 17 at 6:29
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Consider the series
$$sum_{n=1}^infty frac{(-1)^n}{n+x}$$
Find all $x in mathbb{R}$ at which the series converges. Converges absolutely. Find all intervals of $mathbb{R}$ where the series defining $f$ converges uniformly, and all intervals of $mathbb{R}$ on which $f$ is continuous
I'm very confused about how to think about this
real-analysis continuity uniform-continuity
edited Nov 16 at 5:24
Eevee Trainer
97311
asked Nov 16 at 5:08
kiarasaini
61
Consider the series
$$sum_{n=1}^infty frac{(-1)^n}{n+x}$$
Find all $x in mathbb{R}$ at which the series converges. Converges absolutely. Find all intervals of $mathbb{R}$ where the series defining $f$ converges uniformly, and all intervals of $mathbb{R}$ on which $f$ is continuous
I'm very confused about how to think about this
real-analysis continuity uniform-continuity
real-analysis continuity uniform-continuity
edited Nov 16 at 5:24
Eevee Trainer
97311
asked Nov 16 at 5:08
kiarasaini
61
edited Nov 16 at 5:24
Eevee Trainer
97311
asked Nov 16 at 5:08
kiarasaini
61
edited Nov 16 at 5:24
Eevee Trainer
97311
edited Nov 16 at 5:24
Eevee Trainer
97311
edited Nov 16 at 5:24
Eevee Trainer
97311
97311
asked Nov 16 at 5:08
kiarasaini
61
asked Nov 16 at 5:08
kiarasaini
61
asked Nov 16 at 5:08
kiarasaini
61
61
you just need to know the definitions of conditional convergence, absolute convergence, uniform convergence and apply them to your series, it is not so complicate
– Masacroso
Nov 16 at 5:27
Do you know the conditions which guarantee the convergence of an alternating series?
– John Wayland Bales
Nov 16 at 5:28
@JohnWaylandBales it's not quite so simple if I'm not mistaken, at least for $x<0$.
– qbert
Nov 17 at 5:34
@qbert My question was intended to gauge just how confused the OP is. The first two should be easy aside from the negative integers.
– John Wayland Bales
Nov 17 at 6:27
@JohnWaylandBales fair enough and definitely true about the first two and uniform convergence on the nonegatives
– qbert
Nov 17 at 6:29
add a comment |
you just need to know the definitions of conditional convergence, absolute convergence, uniform convergence and apply them to your series, it is not so complicate
– Masacroso
Nov 16 at 5:27
Do you know the conditions which guarantee the convergence of an alternating series?
– John Wayland Bales
Nov 16 at 5:28
@JohnWaylandBales it's not quite so simple if I'm not mistaken, at least for $x<0$.
– qbert
Nov 17 at 5:34
@qbert My question was intended to gauge just how confused the OP is. The first two should be easy aside from the negative integers.
– John Wayland Bales
Nov 17 at 6:27
@JohnWaylandBales fair enough and definitely true about the first two and uniform convergence on the nonegatives
– qbert
Nov 17 at 6:29
you just need to know the definitions of conditional convergence, absolute convergence, uniform convergence and apply them to your series, it is not so complicate
– Masacroso
Nov 16 at 5:27
you just need to know the definitions of conditional convergence, absolute convergence, uniform convergence and apply them to your series, it is not so complicate
– Masacroso
Nov 16 at 5:27
Do you know the conditions which guarantee the convergence of an alternating series?
– John Wayland Bales
Nov 16 at 5:28
Do you know the conditions which guarantee the convergence of an alternating series?
– John Wayland Bales
Nov 16 at 5:28
@JohnWaylandBales it's not quite so simple if I'm not mistaken, at least for $x<0$.
– qbert
Nov 17 at 5:34
@JohnWaylandBales it's not quite so simple if I'm not mistaken, at least for $x<0$.
– qbert
Nov 17 at 5:34
@qbert My question was intended to gauge just how confused the OP is. The first two should be easy aside from the negative integers.
– John Wayland Bales
Nov 17 at 6:27
@qbert My question was intended to gauge just how confused the OP is. The first two should be easy aside from the negative integers.
– John Wayland Bales
Nov 17 at 6:27
@JohnWaylandBales fair enough and definitely true about the first two and uniform convergence on the nonegatives
– qbert
Nov 17 at 6:29
@JohnWaylandBales fair enough and definitely true about the first two and uniform convergence on the nonegatives
– qbert
Nov 17 at 6:29
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3000746%2fconsider-the-series-sum-n-1-infty-frac-1nnx%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
you just need to know the definitions of conditional convergence, absolute convergence, uniform convergence and apply them to your series, it is not so complicate
– Masacroso
Nov 16 at 5:27
Do you know the conditions which guarantee the convergence of an alternating series?
– John Wayland Bales
Nov 16 at 5:28
@JohnWaylandBales it's not quite so simple if I'm not mistaken, at least for $x<0$.
– qbert
Nov 17 at 5:34
@qbert My question was intended to gauge just how confused the OP is. The first two should be easy aside from the negative integers.
– John Wayland Bales
Nov 17 at 6:27
@JohnWaylandBales fair enough and definitely true about the first two and uniform convergence on the nonegatives
– qbert
Nov 17 at 6:29