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Math Help - simple yet clever proof with factorials

  1. #1
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    simple yet clever proof with factorials

    we're supposed to use the principle of mathematical induction for this.



    basically the inductive part boils down to proving algebraically that
    (k+1)!-1+(k+1)\cdot(k+1)!=(k+2)!-1

    but i'm not familiar enough with factorials to show this. i've read about factorials on wikipedia but they didn't have any good identities or anything i could use. any suggestions would be very helpful but for now i'm going to just stare at it for a few minutes and read about series with factorials.

    thanks guys
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  2. #2
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    Quote Originally Posted by hairy View Post
    we're supposed to use the principle of mathematical induction for this.



    basically the inductive part boils down to proving algebraically that
    (k+1)!-1+(k+1)\cdot(k+1)!=(k+2)!-1

    but i'm not familiar enough with factorials to show this. i've read about factorials on wikipedia but they didn't have any good identities or anything i could use. any suggestions would be very helpful but for now i'm going to just stare at it for a few minutes and read about series with factorials.

    thanks guys

    If you already realized that n!=n(n-1)! then it is almost trivial

    (k+1)!-1+(k+1)\cdot(k+1)!=(k+1)!\left[1+k+1\right]-1=(k+1)!(k+2)-1=...
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  3. #3
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    Quote Originally Posted by tonio View Post
    If you already realized that n!=n(n-1)! then it is almost trivial

    (k+1)!-1+(k+1)\cdot(k+1)!=(k+1)!\left[1+k+1\right]-1=(k+1)!(k+2)-1=...


    thanks, i see.
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