The limit of the sequence $lbrace nsin(pi/n) rbrace$ [on hold]

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Let $lbrace a_n rbrace$ be the sequence $lbrace nsin(pi/n) rbrace$. What is the limiting value $lim_nto infty a_n$ ?.



I appreciate any help. Thanks in advance.




sequences-and-series limits




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put on hold as off-topic by Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy Aug 3 at 16:18


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Let $t=dfrac1nto0$.
    – user 108128
    Aug 3 at 16:03














up vote
-3
down vote

favorite












Let $lbrace a_n rbrace$ be the sequence $lbrace nsin(pi/n) rbrace$. What is the limiting value $lim_nto infty a_n$ ?.



I appreciate any help. Thanks in advance.




sequences-and-series limits




share|cite|improve this question











put on hold as off-topic by Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy Aug 3 at 16:18


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Let $t=dfrac1nto0$.
    – user 108128
    Aug 3 at 16:03












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











Let $lbrace a_n rbrace$ be the sequence $lbrace nsin(pi/n) rbrace$. What is the limiting value $lim_nto infty a_n$ ?.



I appreciate any help. Thanks in advance.




sequences-and-series limits




share|cite|improve this question











Let $lbrace a_n rbrace$ be the sequence $lbrace nsin(pi/n) rbrace$. What is the limiting value $lim_nto infty a_n$ ?.



I appreciate any help. Thanks in advance.





sequences-and-series limits





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share|cite|improve this question




share|cite|improve this question









asked Aug 3 at 15:56









Hussein Eid

6




6




put on hold as off-topic by Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy Aug 3 at 16:18


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy Aug 3 at 16:18


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Strants, user 108128, José Carlos Santos, Arnaud Mortier, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Let $t=dfrac1nto0$.
    – user 108128
    Aug 3 at 16:03
















  • Let $t=dfrac1nto0$.
    – user 108128
    Aug 3 at 16:03















Let $t=dfrac1nto0$.
– user 108128
Aug 3 at 16:03




Let $t=dfrac1nto0$.
– user 108128
Aug 3 at 16:03










2 Answers
2






active

oldest

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up vote
0
down vote













Write $$fracsin(fracpin)fracpincdot pi$$






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  • I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
    – Hussein Eid
    Aug 3 at 16:00











  • Yes since we have $$|sin(n)|le 1$$
    – Dr. Sonnhard Graubner
    Aug 3 at 16:00






  • 1




    Are you familiar with Heine definition of a limit of a function?
    – Mark
    Aug 3 at 16:01










  • And what is your Question?
    – Dr. Sonnhard Graubner
    Aug 3 at 16:01










  • That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
    – Mark
    Aug 3 at 16:03

















up vote
0
down vote













Hint: $$lim_xto 0 fracsinxx=1$$.






share|cite|improve this answer






























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    down vote













    Write $$fracsin(fracpin)fracpincdot pi$$






    share|cite|improve this answer





















    • I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
      – Hussein Eid
      Aug 3 at 16:00











    • Yes since we have $$|sin(n)|le 1$$
      – Dr. Sonnhard Graubner
      Aug 3 at 16:00






    • 1




      Are you familiar with Heine definition of a limit of a function?
      – Mark
      Aug 3 at 16:01










    • And what is your Question?
      – Dr. Sonnhard Graubner
      Aug 3 at 16:01










    • That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
      – Mark
      Aug 3 at 16:03














    up vote
    0
    down vote













    Write $$fracsin(fracpin)fracpincdot pi$$






    share|cite|improve this answer





















    • I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
      – Hussein Eid
      Aug 3 at 16:00











    • Yes since we have $$|sin(n)|le 1$$
      – Dr. Sonnhard Graubner
      Aug 3 at 16:00






    • 1




      Are you familiar with Heine definition of a limit of a function?
      – Mark
      Aug 3 at 16:01










    • And what is your Question?
      – Dr. Sonnhard Graubner
      Aug 3 at 16:01










    • That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
      – Mark
      Aug 3 at 16:03












    up vote
    0
    down vote










    up vote
    0
    down vote









    Write $$fracsin(fracpin)fracpincdot pi$$






    share|cite|improve this answer













    Write $$fracsin(fracpin)fracpincdot pi$$







    share|cite|improve this answer













    share|cite|improve this answer



    share|cite|improve this answer











    answered Aug 3 at 15:58









    Dr. Sonnhard Graubner

    66.6k32659




    66.6k32659











    • I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
      – Hussein Eid
      Aug 3 at 16:00











    • Yes since we have $$|sin(n)|le 1$$
      – Dr. Sonnhard Graubner
      Aug 3 at 16:00






    • 1




      Are you familiar with Heine definition of a limit of a function?
      – Mark
      Aug 3 at 16:01










    • And what is your Question?
      – Dr. Sonnhard Graubner
      Aug 3 at 16:01










    • That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
      – Mark
      Aug 3 at 16:03
















    • I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
      – Hussein Eid
      Aug 3 at 16:00











    • Yes since we have $$|sin(n)|le 1$$
      – Dr. Sonnhard Graubner
      Aug 3 at 16:00






    • 1




      Are you familiar with Heine definition of a limit of a function?
      – Mark
      Aug 3 at 16:01










    • And what is your Question?
      – Dr. Sonnhard Graubner
      Aug 3 at 16:01










    • That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
      – Mark
      Aug 3 at 16:03















    I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
    – Hussein Eid
    Aug 3 at 16:00





    I already know that. This holds trivially for functions. Does the rule $lim_nto 0 sin(n)/n=1$ hold for sequences as well?
    – Hussein Eid
    Aug 3 at 16:00













    Yes since we have $$|sin(n)|le 1$$
    – Dr. Sonnhard Graubner
    Aug 3 at 16:00




    Yes since we have $$|sin(n)|le 1$$
    – Dr. Sonnhard Graubner
    Aug 3 at 16:00




    1




    1




    Are you familiar with Heine definition of a limit of a function?
    – Mark
    Aug 3 at 16:01




    Are you familiar with Heine definition of a limit of a function?
    – Mark
    Aug 3 at 16:01












    And what is your Question?
    – Dr. Sonnhard Graubner
    Aug 3 at 16:01




    And what is your Question?
    – Dr. Sonnhard Graubner
    Aug 3 at 16:01












    That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
    – Mark
    Aug 3 at 16:03




    That was a question to Hussein Eid. The reason why this rule works for sequences is because of Heine's definition.
    – Mark
    Aug 3 at 16:03










    up vote
    0
    down vote













    Hint: $$lim_xto 0 fracsinxx=1$$.






    share|cite|improve this answer



























      up vote
      0
      down vote













      Hint: $$lim_xto 0 fracsinxx=1$$.






      share|cite|improve this answer

























        up vote
        0
        down vote










        up vote
        0
        down vote









        Hint: $$lim_xto 0 fracsinxx=1$$.






        share|cite|improve this answer















        Hint: $$lim_xto 0 fracsinxx=1$$.







        share|cite|improve this answer















        share|cite|improve this answer



        share|cite|improve this answer








        edited Aug 3 at 16:37









        Andrew

        2,37221123




        2,37221123











        answered Aug 3 at 15:59









        Mark

        5949




        5949












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