Are these modified harmonic series divergent? The Next CEO of Stack OverflowDifference of harmonic seriesDoes this modified harmonic series converge?Harmonic series principal valueA modification of the terms of the harmonic seriesSign fluctuation in the harmonic series (sum)Kempner's series vs harmonic series (convergent vs divergent series via exclusion)Is this a valid way to prove this modified harmonic series diverges?Prove that the harmonic series $sum_i=1^infty frac1i$ is divergent by using induction?Modified alternating harmonic seriesA question about divergent series related to the harmonic series
Is it ever safe to open a suspicious html file (e.g. email attachment)?
A "random" question: usage of "random" as adjective in Spanish
How did the Bene Gesserit know how to make a Kwisatz Haderach?
Workaholic Formal/Informal
"and that skill is always a class skill for you" - does "always" have any meaning in Pathfinder?
Is there a way to save my career from absolute disaster?
Example of a Mathematician/Physicist whose Other Publications during their PhD eclipsed their PhD Thesis
What does convergence in distribution "in the Gromov–Hausdorff" sense mean?
FBX seems to be empty when imported into Blender
If/When UK leaves the EU, can a future goverment conduct a referendum to join the EU?
How do I go from 300 unfinished/half written blog posts, to published posts?
What is the result of assigning to std::vector<T>::begin()?
How to make a variable always equal to the result of some calculations?
Preparing Indesign booklet with .psd graphics for print
If the heap is initialized for security, then why is the stack uninitialized?
Why do airplanes bank sharply to the right after air-to-air refueling?
Can we say or write : "No, it'sn't"?
At which OSI layer a user-generated data resides?
How to transpose the 1st and -1th levels of arbitrarily nested array?
Written every which way
I believe this to be a fraud - hired, then asked to cash check and send cash as Bitcoin
How do scammers retract money, while you can’t?
What connection does MS Office have to Netscape Navigator?
multiple labels for a single equation
Are these modified harmonic series divergent?
The Next CEO of Stack OverflowDifference of harmonic seriesDoes this modified harmonic series converge?Harmonic series principal valueA modification of the terms of the harmonic seriesSign fluctuation in the harmonic series (sum)Kempner's series vs harmonic series (convergent vs divergent series via exclusion)Is this a valid way to prove this modified harmonic series diverges?Prove that the harmonic series $sum_i=1^infty frac1i$ is divergent by using induction?Modified alternating harmonic seriesA question about divergent series related to the harmonic series
$begingroup$
If a new series is formed by taking every $nmathrmth$ term (eg for $n=3$, the 3rd, 6th, 9th etc terms) of the harmonic series$$sum_k=1^inftyfrac1k=frac11+frac12+frac13+cdots$$ is this new series divergent?
sequences-and-series
asked 2 days ago
Peter4075Peter4075
441521
$endgroup$
add a comment |
$begingroup$
If a new series is formed by taking every $nmathrmth$ term (eg for $n=3$, the 3rd, 6th, 9th etc terms) of the harmonic series$$sum_k=1^inftyfrac1k=frac11+frac12+frac13+cdots$$ is this new series divergent?
sequences-and-series
asked 2 days ago
Peter4075Peter4075
441521
$endgroup$
3
$begingroup$
Yes it is. For example, for $n=3$, you have $$frac13+frac16+frac19+frac112 +cdots = frac13 left( frac11+frac12+frac13+frac14+ cdots right) = infty $$
$endgroup$
– Crostul
2 days ago
$begingroup$
Whoops, I should have seen that coming. If you make that comment an answer, I'll happily accept it :-)
$endgroup$
– Peter4075
2 days ago
add a comment |
$begingroup$
If a new series is formed by taking every $nmathrmth$ term (eg for $n=3$, the 3rd, 6th, 9th etc terms) of the harmonic series$$sum_k=1^inftyfrac1k=frac11+frac12+frac13+cdots$$ is this new series divergent?
sequences-and-series
asked 2 days ago
Peter4075Peter4075
441521
$endgroup$
If a new series is formed by taking every $nmathrmth$ term (eg for $n=3$, the 3rd, 6th, 9th etc terms) of the harmonic series$$sum_k=1^inftyfrac1k=frac11+frac12+frac13+cdots$$ is this new series divergent?
sequences-and-series
sequences-and-series
asked 2 days ago
Peter4075Peter4075
441521
asked 2 days ago
Peter4075Peter4075
441521
asked 2 days ago
Peter4075Peter4075
441521
asked 2 days ago
Peter4075Peter4075
441521
asked 2 days ago
Peter4075Peter4075
441521
441521
3
$begingroup$
Yes it is. For example, for $n=3$, you have $$frac13+frac16+frac19+frac112 +cdots = frac13 left( frac11+frac12+frac13+frac14+ cdots right) = infty $$
$endgroup$
– Crostul
2 days ago
$begingroup$
Whoops, I should have seen that coming. If you make that comment an answer, I'll happily accept it :-)
$endgroup$
– Peter4075
2 days ago
add a comment |
3
$begingroup$
Yes it is. For example, for $n=3$, you have $$frac13+frac16+frac19+frac112 +cdots = frac13 left( frac11+frac12+frac13+frac14+ cdots right) = infty $$
$endgroup$
– Crostul
2 days ago
$begingroup$
Whoops, I should have seen that coming. If you make that comment an answer, I'll happily accept it :-)
$endgroup$
– Peter4075
2 days ago
3
3
$begingroup$
Yes it is. For example, for $n=3$, you have $$frac13+frac16+frac19+frac112 +cdots = frac13 left( frac11+frac12+frac13+frac14+ cdots right) = infty $$
$endgroup$
– Crostul
2 days ago
$begingroup$
Yes it is. For example, for $n=3$, you have $$frac13+frac16+frac19+frac112 +cdots = frac13 left( frac11+frac12+frac13+frac14+ cdots right) = infty $$
$endgroup$
– Crostul
2 days ago
$begingroup$
Whoops, I should have seen that coming. If you make that comment an answer, I'll happily accept it :-)
$endgroup$
– Peter4075
2 days ago
$begingroup$
Whoops, I should have seen that coming. If you make that comment an answer, I'll happily accept it :-)
$endgroup$
– Peter4075
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Yes, it is. For example, for $n=3$, you have
$$frac13+ frac16+ frac19+ frac112+ cdots = frac13 left(
frac11+ frac12+ frac13+ frac14+ cdotsright) = infty$$
answered 2 days ago
CrostulCrostul
28.2k22352
$endgroup$
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
);
);
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%2f3164599%2fare-these-modified-harmonic-series-divergent%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
$begingroup$
Yes, it is. For example, for $n=3$, you have
$$frac13+ frac16+ frac19+ frac112+ cdots = frac13 left(
frac11+ frac12+ frac13+ frac14+ cdotsright) = infty$$
answered 2 days ago
CrostulCrostul
28.2k22352
$endgroup$
add a comment |
$begingroup$
Yes, it is. For example, for $n=3$, you have
$$frac13+ frac16+ frac19+ frac112+ cdots = frac13 left(
frac11+ frac12+ frac13+ frac14+ cdotsright) = infty$$
answered 2 days ago
CrostulCrostul
28.2k22352
$endgroup$
add a comment |
$begingroup$
Yes, it is. For example, for $n=3$, you have
$$frac13+ frac16+ frac19+ frac112+ cdots = frac13 left(
frac11+ frac12+ frac13+ frac14+ cdotsright) = infty$$
answered 2 days ago
CrostulCrostul
28.2k22352
$endgroup$
Yes, it is. For example, for $n=3$, you have
$$frac13+ frac16+ frac19+ frac112+ cdots = frac13 left(
frac11+ frac12+ frac13+ frac14+ cdotsright) = infty$$
answered 2 days ago
CrostulCrostul
28.2k22352
answered 2 days ago
CrostulCrostul
28.2k22352
answered 2 days ago
CrostulCrostul
28.2k22352
answered 2 days ago
CrostulCrostul
28.2k22352
28.2k22352
add a comment |
add a comment |
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.
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%2f3164599%2fare-these-modified-harmonic-series-divergent%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
3
$begingroup$
Yes it is. For example, for $n=3$, you have $$frac13+frac16+frac19+frac112 +cdots = frac13 left( frac11+frac12+frac13+frac14+ cdots right) = infty $$
$endgroup$
– Crostul
2 days ago
$begingroup$
Whoops, I should have seen that coming. If you make that comment an answer, I'll happily accept it :-)
$endgroup$
– Peter4075
2 days ago