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Thread: Show that : n = E (n * (1 + LOG ((n) -LOG (1 + n)) + 1) with n strictly positive integer

  1. #1 Show that : n = E (n * (1 + LOG ((n) -LOG (1 + n)) + 1) with n strictly positive integer 
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    HI,


    Show that n = E ((n * (1 + LOG (n) -LOG (1 + n)) + 1)
    With n is a strictly positive integer
    and E is an integer (The ENT function on Excel).


    Last edited by Math10; September 30th, 2020 at 10:02 PM.
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  3. #2  
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    Check your parentheses. Should it be (log(n)-log(n+1))?


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  4. #3  
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    tanks you n = E ((n * (1 + LOG (n) -LOG (1 + n)) + 1)
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  5. #4  
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    I have to check that n<=((n * (1 + LOG (n) -LOG (1 + n)) + 1) <n+1 to define the integer part
    but n#((n * (1 + LOG (n) -LOG (1 + n)) + 1).


    et and I can demonstrate that n<((n * (1 + LOG (n) -LOG (1 + n)) + 1) <n+1 So I can't define the integer part.
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  6. #5  
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    By definition if n<x<n+1 then the integer part of x is n. Therefore you are done.
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