Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof by strong mathematical induction, can you see if this is enough to conclude?

  1. Oct 2, 2006 #1
    Hello everyone.

    THis is my first proof to strong mathematical induction so im' not sure if its correct or not it seems it though but then again I wrote it. Any suggestions/corrections would be great! THanks

    Here it is!
    http://suprfile.com/src/1/3j34eh1/lastscan.jpg [Broken]
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 3, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    Your inductive hypothesis is that [tex]e_i\leq 3^i[/tex] for i=1,2,..,k-1, but you used:
    [tex]e_{k-1}\leq 3^k[/tex]
    [tex]e_{k-2}\leq 3^k[/tex]
    [tex]e_{k-3}\leq 3^k[/tex]

    That is certainly true, but not strong enough to conclude that
    [tex]e_{k}\leq 3^k[/tex]

    What if [tex]e_{k-1}=e_{k-2}=e_{k-3}= 3^k[/tex], then your three inequalities hold, but [itex]e_k=3^{k+1}[/itex]. You need to use your inductive hypothesis more strongly.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook