Mixing
Divergent condition of a series.
-2
$begingroup$
For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$
real-analysis sequences-and-series divergent-series
asked Jan 15 at 14:36
MathRockMathRock
316
$endgroup$
add a comment |
-2
$begingroup$
For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$
real-analysis sequences-and-series divergent-series
asked Jan 15 at 14:36
MathRockMathRock
316
$endgroup$
1
$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45
add a comment |
-2
-2
-2
$begingroup$
For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$
real-analysis sequences-and-series divergent-series
asked Jan 15 at 14:36
MathRockMathRock
316
$endgroup$
For $s>0$ when the following series will diverge $$sum_{k=1}bigg(frac{2^k}{1+2^k}bigg)^{2s}.$$
real-analysis sequences-and-series divergent-series
real-analysis sequences-and-series divergent-series
asked Jan 15 at 14:36
MathRockMathRock
316
asked Jan 15 at 14:36
MathRockMathRock
316
asked Jan 15 at 14:36
MathRockMathRock
316
asked Jan 15 at 14:36
MathRockMathRock
316
asked Jan 15 at 14:36
MathRockMathRock
316
316
1
$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45
add a comment |
1
$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45
1
1
$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45
$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
Hint: what happens to the summand as $k$ gets large?
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
$endgroup$
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
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%2f3074509%2fdivergent-condition-of-a-series%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
$begingroup$
Hint: what happens to the summand as $k$ gets large?
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
$endgroup$
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
add a comment |
1
$begingroup$
Hint: what happens to the summand as $k$ gets large?
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
$endgroup$
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
add a comment |
1
1
1
$begingroup$
Hint: what happens to the summand as $k$ gets large?
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
$endgroup$
Hint: what happens to the summand as $k$ gets large?
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
answered Jan 15 at 14:37
Robert IsraelRobert Israel
324k23214468
324k23214468
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
add a comment |
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Can you say more??
$endgroup$
– MathRock
Jan 15 at 14:41
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
$begingroup$
Look up the divergence test.
$endgroup$
– Tom Himler
Jan 15 at 15:22
add a comment |
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
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%2f3074509%2fdivergent-condition-of-a-series%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
1
$begingroup$
We would love to see your attempts too, try some manipulation of terms.
$endgroup$
– Akshar Gandhi
Jan 15 at 14:45