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

More trouble with induction

  1. Jun 8, 2005 #1
    A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1. Show that Ci=32i for i greater than or equal to 0.

    I wasn't to clear on what it meant by this, so what I have is that I am trying to show that Zk = Ci. Is that correct?

    From there, I proved the base case to be true.

    Proving n+1 to be true is where I am having problems.
    Cn+1=(Cn)2 and
    Zn+1=32n+1=32n(2)

    I don't see how I can express Cn+1 to be like Zn+1. I'm not even sure if I am understanding the problem correctly. Am I at least going in the right direction? Any hints?
     
  2. jcsd
  3. Jun 8, 2005 #2
    Is this to be done using "Strong Induction"
    I was using basic mathematical induction.
     
  4. Jun 8, 2005 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper


    We dont' know. You're the one that introduced Ci without explaining what it is.
     
  5. Jun 8, 2005 #4
    Here's how far I've gotten now,
    I'm trying to show that Ck+1=32k+1.

    By definition,
    Ck+1
    = (Ck)2
    = (32k)2 By the Induction Hypothesis
    = (32k(2))
    = (32k+1)

    Is that correct?
     
  6. Jun 8, 2005 #5
    The very first sentence is straight from my textbook. I'm guessing Ci is just another way of representing Zk.
     
  7. Jun 8, 2005 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "The very first sentence" was "A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1." which says nothing about Ci. You can't prove anything about Ci without knowing exactly how it is defined!
     
  8. Jun 8, 2005 #7
    "A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1. Show that Ci=32i for i greater than or equal to 0."

    I e-mailed my professor, he said it is supposed to be Zi, not C... I don't know if that helps...
     
  9. Jun 8, 2005 #8

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    It helps and makes it easy; just do it. And if you can't write saying where you're stuck.
     
  10. Jun 8, 2005 #9
    I'm still fixated on this. :biggrin: Maybe if I make the Cs Zs instead?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: More trouble with induction
  1. Induction Proof (Replies: 4)

  2. Proof by induction (Replies: 4)

  3. Induction method (Replies: 1)

Loading...