? 發問於 科學及數學數學 · 1 十年 前

Can 8n*3-2n divided by6?

Can 8n*3-2n divided by6?

Why

更新:

THANK you

i am form 2 these year and quite good at maths

my principal give our class some question like it and want us to proof them

so

i'm extremly happy to recieved your answer

3 個解答

評分
  • 1 十年 前
    最佳解答

    I persume that n is a positive integer in your expression.

    By MI,

    圖片參考:http://i238.photobucket.com/albums/ff245/chocolate...

    2008-09-04 19:40:08 補充:

    But then, your n could be a negative integer as well, so you may verify the result by factorization:

    8n^3 - 2n = 2n ( 4n^2 - 1 ) = 2n ( 2n + 1 )( 2n - 1 )

    2008-09-04 19:40:12 補充:

    For any 3 consecutive integers, at least one of them is a multiple of 2 and one of them must be a multiple of 3, hence 2n ( 2n + 1 )( 2n - 1 ) is divisible by 6, n being an integer.

    2008-09-04 20:19:44 補充:

    我覺得係三次方, 如果唔係根本就冇得做!

    2008-09-08 22:12:59 補充:

    So, if you are only Form 2 and have not learnt anything about MI, just look at the method of factorization as shown above.

    資料來源: My Maths Knowledge
  • 1 十年 前

    to發問者:

    如果你個*係代表乘,咁第一個ans係岩

    如果個*代表次方,咁第二個ans係岩

  • 1 十年 前

    Let P(n) be the proposition'8n*3-2n' divided by6.

     When n=1

        =8(1).3-2(1)

        =22

    ∴(8n*3-2n) can not divided by6.

    資料來源: 自己
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