Infinite series sum

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












What is the sum of $$sumlimits_n=1^inftycos((2n-1)x)$$ and what is
$$sumlimits_n=0^inftycos(2nx)$$
I have got the infinte series sum of $cos x$ but didn't know how to get that.










share|cite|improve this question























  • I have edited your question. Please format your questions as I did with LaTeX or MathJax
    – Ahmad Bazzi
    Sep 11 at 3:06






  • 2




    and what is the " ... infinte series sum of $cos x$ ... " ?
    – Ahmad Bazzi
    Sep 11 at 3:15














up vote
0
down vote

favorite












What is the sum of $$sumlimits_n=1^inftycos((2n-1)x)$$ and what is
$$sumlimits_n=0^inftycos(2nx)$$
I have got the infinte series sum of $cos x$ but didn't know how to get that.










share|cite|improve this question























  • I have edited your question. Please format your questions as I did with LaTeX or MathJax
    – Ahmad Bazzi
    Sep 11 at 3:06






  • 2




    and what is the " ... infinte series sum of $cos x$ ... " ?
    – Ahmad Bazzi
    Sep 11 at 3:15












up vote
0
down vote

favorite









up vote
0
down vote

favorite











What is the sum of $$sumlimits_n=1^inftycos((2n-1)x)$$ and what is
$$sumlimits_n=0^inftycos(2nx)$$
I have got the infinte series sum of $cos x$ but didn't know how to get that.










share|cite|improve this question















What is the sum of $$sumlimits_n=1^inftycos((2n-1)x)$$ and what is
$$sumlimits_n=0^inftycos(2nx)$$
I have got the infinte series sum of $cos x$ but didn't know how to get that.







sequences-and-series






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 11 at 3:05









Ahmad Bazzi

7,4912724




7,4912724










asked Sep 11 at 3:02









Sweta

254




254











  • I have edited your question. Please format your questions as I did with LaTeX or MathJax
    – Ahmad Bazzi
    Sep 11 at 3:06






  • 2




    and what is the " ... infinte series sum of $cos x$ ... " ?
    – Ahmad Bazzi
    Sep 11 at 3:15
















  • I have edited your question. Please format your questions as I did with LaTeX or MathJax
    – Ahmad Bazzi
    Sep 11 at 3:06






  • 2




    and what is the " ... infinte series sum of $cos x$ ... " ?
    – Ahmad Bazzi
    Sep 11 at 3:15















I have edited your question. Please format your questions as I did with LaTeX or MathJax
– Ahmad Bazzi
Sep 11 at 3:06




I have edited your question. Please format your questions as I did with LaTeX or MathJax
– Ahmad Bazzi
Sep 11 at 3:06




2




2




and what is the " ... infinte series sum of $cos x$ ... " ?
– Ahmad Bazzi
Sep 11 at 3:15




and what is the " ... infinte series sum of $cos x$ ... " ?
– Ahmad Bazzi
Sep 11 at 3:15










1 Answer
1






active

oldest

votes

















up vote
2
down vote













Since $a_n = cos 2nx $ does not go to zero. So
$$sumlimits_n=0^infty cos 2nx $$
diverges. What can you say about the other sum ?






share|cite|improve this answer




















    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',
    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


















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2912693%2finfinite-series-sum%23new-answer', 'question_page');

    );

    Post as a guest






























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote













    Since $a_n = cos 2nx $ does not go to zero. So
    $$sumlimits_n=0^infty cos 2nx $$
    diverges. What can you say about the other sum ?






    share|cite|improve this answer
























      up vote
      2
      down vote













      Since $a_n = cos 2nx $ does not go to zero. So
      $$sumlimits_n=0^infty cos 2nx $$
      diverges. What can you say about the other sum ?






      share|cite|improve this answer






















        up vote
        2
        down vote










        up vote
        2
        down vote









        Since $a_n = cos 2nx $ does not go to zero. So
        $$sumlimits_n=0^infty cos 2nx $$
        diverges. What can you say about the other sum ?






        share|cite|improve this answer












        Since $a_n = cos 2nx $ does not go to zero. So
        $$sumlimits_n=0^infty cos 2nx $$
        diverges. What can you say about the other sum ?







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Sep 11 at 3:17









        Ahmad Bazzi

        7,4912724




        7,4912724



























             

            draft saved


            draft discarded















































             


            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2912693%2finfinite-series-sum%23new-answer', 'question_page');

            );

            Post as a guest













































































            這個網誌中的熱門文章

            How to combine Bézier curves to a surface?

            Mutual Information Always Non-negative

            Why am i infinitely getting the same tweet with the Twitter Search API?