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Emma Watson

19/03/2017 at 15:47
Answers
3
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Today is Sunday. On which day of the week is 13 + 23 + 33 + ... + 20083 days later from tomorrow?


divisibility


    List of answers
  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:19

    We have (n-1)n(n+1)=(n^2-n)(n+1)=(n^2-n)n+n^2-n=n^3-n^2+n^2-n

             =n^3-n

    \Rightarrow n^3=(n-1)n(n+1)+n (1)

    Apply (1) to the expression, we have : 13 + 23 + 33 + ... + 20083 

    = (1 - 1)1(1 + 1) + 1 + (2 - 2)2(2 + 2) + 2 + ....... + (2008 - 2008) 2008 (2008 - 2008) + 2008

    = 1 + 2 + 1.2.3 + 3 + 2.3.4 + ........ + 2008 + 2007.2008.2009

    = (1 + 2 + 3 + ...... + 2008) + (1.2.3 + 2.3.4 + ...... + 2007.2008.2009)

    = 2017036 + 2007.2008.2009.2010 / 4 

    = The number to mik not count 

  • ...
    ¤« 03/04/2018 at 13:40

    We have  [(n-1)n(n+1)=(n^2-n)(n+1)=(n^2-n)n+n^2-n=n^3-n^2+n^2-n]

              [=n^3-n]

    [\Rightarrow n^3=(n-1)n(n+1)+n]   [(1)]

    Apply (1) to the expression, we have : 13 + 23 + 33 + ... + 20083 

    = (1 - 1)1(1 + 1) + 1 + (2 - 2)2(2 + 2) + 2 + ....... + (2008 - 2008) 2008 (2008 - 2008) + 2008

    = 1 + 2 + 1.2.3 + 3 + 2.3.4 + ........ + 2008 + 2007.2008.2009

    = (1 + 2 + 3 + ...... + 2008) + (1.2.3 + 2.3.4 + ...... + 2007.2008.2009)

    = 2017036 + 2007.2008.2009.2010 / 4 

    = The number to mik not count

  • ...
    Love people Name Jiang 20/03/2017 at 17:43

    We have (n-1)n(n+1)=(n^2-n)(n+1)=(n^2-n)n+n^2-n=n^3-n^2+n^2-n

             =n^3-n

    \Rightarrow n^3=(n-1)n(n+1)+n (1)

    Apply (1) to the expression, we have : 13 + 23 + 33 + ... + 20083 

    = (1 - 1)1(1 + 1) + 1 + (2 - 2)2(2 + 2) + 2 + ....... + (2008 - 2008) 2008 (2008 - 2008) + 2008

    = 1 + 2 + 1.2.3 + 3 + 2.3.4 + ........ + 2008 + 2007.2008.2009

    = (1 + 2 + 3 + ...... + 2008) + (1.2.3 + 2.3.4 + ...... + 2007.2008.2009)

    = 2017036 + 2007.2008.2009.2010 / 4 

    = The number to mik not count 


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