Hãy tính M = 2^2010 – (2^2009 + 2^2008 + …. + 2^1 + 2^0).

Question

Hãy tính M = 2^2010 – (2^2009 + 2^2008 + …. + 2^1 + 2^0).

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Dulcie 1 year 2020-10-14T05:12:38+00:00 2 Answers 89 views 0

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    0
    2020-10-14T05:14:02+00:00

    `Answer :`

    `M = 2^2010 – (2^2009 + 2^2008 + …. + 2^1 + 2^0)`

    Ta có : Đặt `A = (2^2009 + 2^2008 + …. + 2^1 + 2^0)`

    `=> A = 2^2009 + 2^2008 + …. + 2^1 + 2^0`

    `= 2^0+ 2^1 + …. + 2^2008 + 2^2009`

    Nhân `2` với `A` : 

    `=> 2A = 2 +2^2 +….+2^2009 + 2^2010`

    `2A -A = ( 2 +2^2 +….+2^2009 + 2^2010) – (2^0+ 2^1 + …. + 2^2008 + 2^2009)`

    `=> A = 1 – 2^2010`

    `=> M = 2^2010 – 1-2^2010`

    `=> M = -1 `

    0
    2020-10-14T05:14:27+00:00

    Đặt `N=2^2009 + 2^2008 + …. + 2^1 + 2^0`

    `N=2^0+2^1+…+2^2008+2^2009`

    `2N=2+2^2+…+2^2009+2^2010`

    `2N-N=2^2010-1`

    `N=2^2010-1`

    `M=2^2010-N`

    `M=2^2010-2^2010-1`

    `M=-1`

     

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