1.不用計算機,計算出(+1)+(-2)+(+3)+(-4)+…+(+99)+(-100)的值,簡述你所用的方法
2.方程x-2x+3x-4x+5x-6x+…+99x-100x=200。解此方程,並簡述你所用的方法
3.展開數式(x-1)(x^99次方+x^98次方+x^97次方+…+x^2次方+x+1)共有多少項?簡述你所用的方法
plz help me~~
maths~
2010-08-02 9:40 pm
回答 (2)
2010-08-03 10:16 pm
✔ 最佳答案
1. 從數列規律:(+1)+(-2) = -1
(+1)+(-2)+(+3)+(-4) = (-1)+(-1) = -2
(+1)+(-2)+(+3)+(-4)+(+5)+(-6) = (-1)+(-1)+(-1) = -3
由此可觀察到, 每兩項會產生一個(-1), 所以100項會有50個(-1), 因此,
(+1)+(-2)+(+3)+(-4)+…+(+99)+(-100) = -50
2.
x-2x+3x-4x+5x-6x+…+99x-100x = 200
(1-2+3-4+5-6+…+99-100)x = 200
從上題, -50x = 200
x = -4
3. 從數列規律:
(x-1)(x+1) = x^2 - 1
(x-1)(x^2+x+1) = x^3 -1
(x-1)(x^3+x^2+x+1) = x^4 -1
由此可觀察到,
(x-1)(x^99+x^98+x^97+…+x^2+x+1) = x^100 -1
所以會有兩項.
參考: ME
2010-08-02 9:56 pm
1.首先1+(-2)+3-4+5-6+7-8+9...-98+99-100
=1+(3-2)+(5-4)+(7-6)+(9-8)...(99-98)-100
=1+93*1-100
=94-100
=-6
2.同上題差不多
x-2x+3x-4x+5x...+99x-100x=200
x+93x-100x=200
96x=200
x=25/12
第三題唔明
=1+(3-2)+(5-4)+(7-6)+(9-8)...(99-98)-100
=1+93*1-100
=94-100
=-6
2.同上題差不多
x-2x+3x-4x+5x...+99x-100x=200
x+93x-100x=200
96x=200
x=25/12
第三題唔明
參考: me~
收錄日期: 2021-04-20 22:18:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100802000051KK00743