Can 8n*3-2n divided by6?
Can 8n*3-2n divided by6?
Why
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
- Gabriella MontezLv 71 十年 前最佳解答
I persume that n is a positive integer in your expression.
By MI,
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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
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