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Thread: Is this induction correct/?

  1. #1
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    Is this induction correct/?

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    Re: Is this induction correct/?

    Here is a list of $k!$ for $k=0,1,2,3,4,5,6,7$

    $\{1,1,2,6,24,120,720,5040\}$

    and a list of $3^k$ for $k=0,1,2,3,4,5,6,7$

    $\{1,3,9,27,81,243,729,2187\}$
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    Re: Is this induction correct/?

    so there is something wrong with your induction proof
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    Re: Is this induction correct/?

    But isn't that what I did? I expressed (k+1)! in terms of 3^(k+1)

    so I essentially showed that 3k! is greater than or equal to 3^(k+1).. which is correct, no?
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    Re: Is this induction correct/?

    Quote Originally Posted by math951 View Post
    But isn't that what I did? I expressed (k+1)! in terms of 3^(k+1)
    so I essentially showed that 3k! is greater than or equal to 3^(k+1).. which is correct, no?
    Look at this calculation.
    It appears that your base case is off.
    So if $n\ge 7$ then $n!>3^n$.
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    Re: Is this induction correct/?

    Okay I see...so the whole point was is that they wanted me to find the integer where the inequality holds true.
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