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How to solve by induction or any other method? [on hold]


Mathematical induction question: why can we “assume $P(k)$ holds”?Induction proof of boundedness of a sequenceStrong induction doesn't require a base case?Infinite descent method and strong inductionHow to generalize induction from this definition?Natural numbers but without induction?Use an induction argument to prove that for any natural number $n$, the interval $(n,n+1)$ does not contain any natural number.Proof by “continuous induction”Induction: Prove that any integer postage greater than 34 cents can be formed using only 5-cent and 9-cent stampsIs the induction principle still viable if the induction skips over, or does not hold for some numbers?













-3












$begingroup$


Determine (with proof) the set of natural numbers for which the following inequalities hold.



  1. $3^n+1 > n^4$

  2. $n^3 + (n + 1)^3 > (n + 2)^3$









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put on hold as off-topic by Saad, Arthur, Peter, sdcvvc, Claude Leibovici Mar 11 at 11:24


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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Arthur, Peter, sdcvvc, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.




















    -3












    $begingroup$


    Determine (with proof) the set of natural numbers for which the following inequalities hold.



    1. $3^n+1 > n^4$

    2. $n^3 + (n + 1)^3 > (n + 2)^3$









    share|cite|improve this question









    New contributor




    JP3112 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$



    put on hold as off-topic by Saad, Arthur, Peter, sdcvvc, Claude Leibovici Mar 11 at 11:24


    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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Arthur, Peter, sdcvvc, Claude Leibovici
    If this question can be reworded to fit the rules in the help center, please edit the question.


















      -3












      -3








      -3





      $begingroup$


      Determine (with proof) the set of natural numbers for which the following inequalities hold.



      1. $3^n+1 > n^4$

      2. $n^3 + (n + 1)^3 > (n + 2)^3$









      share|cite|improve this question









      New contributor




      JP3112 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      Determine (with proof) the set of natural numbers for which the following inequalities hold.



      1. $3^n+1 > n^4$

      2. $n^3 + (n + 1)^3 > (n + 2)^3$






      induction






      share|cite|improve this question









      New contributor




      JP3112 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      JP3112 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited Mar 11 at 10:47









      Gurjinder

      554417




      554417






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      asked Mar 11 at 10:31









      JP3112JP3112

      12




      12




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      New contributor





      JP3112 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      JP3112 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.




      put on hold as off-topic by Saad, Arthur, Peter, sdcvvc, Claude Leibovici Mar 11 at 11:24


      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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Arthur, Peter, sdcvvc, Claude Leibovici
      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 Saad, Arthur, Peter, sdcvvc, Claude Leibovici Mar 11 at 11:24


      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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Arthur, Peter, sdcvvc, Claude Leibovici
      If this question can be reworded to fit the rules in the help center, please edit the question.




















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