這幾條數學題我唔識做,有冇人可以幫下手?
1)Consider the equation x - 2x + 3x -4x+ 5x - 6x + ... + 99x -100x = 200. Solve the
equation and briefly explain how you can solve it.
2)How many terms are there when we expend the expression
(x - 1)(x99 + x98 + x97 + ... + x2 + x + 1)?
Briefly explain your answer.
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x99 , x98 , x97 , x2 是指 x 的 99 次方 , 98 次方 , 97 次方 , 2 次方 , 也就是指x乘以x 乘以 x 乘以 99 次.
2x , 3x , 4x , 5x , 6x , 99x ,100x 是指 2 乘以 x ,3 乘以 x ,4 乘以 x ......
請用英文回答 , THX .
請問以下的幾條數學題點做?
2012-08-26 4:59 am
回答 (3)
2012-08-26 5:22 am
✔ 最佳答案
1)x - 2x + 3x - 4x + 5x - 6x + ... + 99x -100x = 200
(x - 2x) + (3x - 4x) + (5x - 6x) + ... + (99x -100x) = 200
In the above equation, there are 50 pairs of brackets on the left hand side,
and the value inside each pair of brackets is equal to -x.
Then 50(-x) = 200
-50x = 200
x = -4
2)
(x - 1)(x^99 + x^98 + x^97 + ... + 1)
= x(x^99 + x^98 + x^97 + ... + 1) - (x^99 + x^98 + x^97 + ..... + 1)
= (x^100 + x^99 + x^98 + x^97 + ... + x) - (x^99 + x^98 + x^97 + ... + x + 1)
= x^100 + (x^99 + x^98 + x^97 + ... + x) - (x^99 + x^98 + x^97 + ... + x) - 1
= x^100 - 1
There are 2terms.
參考: fooks
2012-08-26 8:07 pm
試展開幾項便明了,分項來做較為明白
2012-08-26 5:27 am
fooks答對了...仲以為有得答添，比人答左
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