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Proving inequality with mathematical induction

  1. Mar 4, 2012 #1
    I am having trouble proving these. I cannot figure out how to get to the conclusion. Here is my attempt. The stuff in red is just side work and is not part of the proof. I always get stuck on these types of problems, can someone offer some tips on how to approach these kind of problems in general? Should I start with the right hand side or the left hand side of the inequality?

  2. jcsd
  3. Mar 4, 2012 #2


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    The goal is to show that 5k+1+9<6k+1. A good place to start is to note that 6k+1 = 6*6k > 6*(5k+9) by the inductive hypothesis like your sidework does. Then it suffices to show that
    5k+1+9 < 6(5k+9)
  4. Mar 4, 2012 #3
    I think I got it. So,
    5k+1 +9 < 6(5k+9)
    5*5k + 9 < 6*5k + 54
    5*5k < 6 * 5k since 5 < 6
    5*5k + 9 < 6 * 5k + 54 since 9<54

    Does this look right?
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