1. Can you find the value of the expression (+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)
without using a calculator? Briefly explain how you can do it.
2. Consider the equation x-2x+3x-4x+5x-6x+...+99x-100x=200.Solve the
equation and briefly explain how you can do it.
3.How many terms are there when we expand the expression
(x-1)(x^99+x^98+x^97+...+x^2+x+1)?Briefly explain your answer.
4.Program X is a series of command to control the movement of a robot. The detail of program X is as follows:
-----Program start------
Step1: Move 4 units to the right.
Step2: Move 5 units upwards.
Step3: Move 3 units to the left.
Step4: Move 5 units downwards.
-----Program end-------
Initially the robot was at (0,0). After running program X for 99 times, the battery level can support the robot to complete 2 more step only. Then the robot stopped. Where did the robot stop? Show the step how you find the coordinates.
數學難題f1
2010-07-29 1:47 am
回答 (2)
2010-07-29 8:07 am
✔ 最佳答案
o係意見寫 過左字數限制.. 唯有選擇回答....其實
Ng第3題錯左 應該系得2個terms
(x-1)(x^99+x^98+x^97+...+x^2+x+1)
=x(x^99+x^98+x^97+...+x^2+x+1) - (x^99+x^98+x^97+...+x^2+x+1)
=x^100+x^99+x^98+...+x^3+x^2+x - (x^99+x^98+x^97+...+x^2+x+1)
=x^100 -1
用直式表示個Expansion會清楚D:
x^100 + x^99 + x^98 + x^97 + ... + x^3 + x^2 + x
-) x^99 + x^98 + x^97 + ... + x^3 + x^2 + x +1
-------------------------------------------------------------------------------------
x^100 -1
中間果D (↑) 會約晒, 得番x^100-1
其實(延伸),
x^n-1 = (x-1)[x^(n-1)+x^(n-2)+...+x+1] (n 系 natural number)
循例答番其他果幾題..=.=
1)
(+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)
= (1-2)+(3-4)+(5-6)+...+(99-100)
= 50(-1)
=-50
2) x-2x+3x-4x+5x-6x+...+99x-100x=200
x(1-2+3-4+5-6+...+99-100)=200
-50x=200
x=-4
4) 每run個program, x-coordinate會: +4-3=+1unit ; y-coordinate會: +5-5=冇郁過
run左99次之後, 個robot應該在(99,0), 行多兩個step,變左 (99+4,0+5)=(103,5)
2010-07-29 4:07 am
1. (+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)
(+1)+(-2) = -1
(+3)+(-4) = -1
....
每2個2個加埋, 全部都是-1
共有50個-1, 答案即-50
2. x-2x+3x-4x+5x-6x+...+99x-100x=200
x-2x = -x
3x-4x = -x
.......
每2個2個加埋, 全部都是-x
共有50個-x, 答案即-50x
3. (x - 1) 有 2 terms (中文: 2項, 即 +x 及 - 1)
(x^99+x^98+x^97+...+x^2+x+1)有 100 terms (中文: 100項)
2terms 乘 100terms = 200terms (答案是200terms)
4. 用格仔紙畫下, 自己試下推理
(+1)+(-2) = -1
(+3)+(-4) = -1
....
每2個2個加埋, 全部都是-1
共有50個-1, 答案即-50
2. x-2x+3x-4x+5x-6x+...+99x-100x=200
x-2x = -x
3x-4x = -x
.......
每2個2個加埋, 全部都是-x
共有50個-x, 答案即-50x
3. (x - 1) 有 2 terms (中文: 2項, 即 +x 及 - 1)
(x^99+x^98+x^97+...+x^2+x+1)有 100 terms (中文: 100項)
2terms 乘 100terms = 200terms (答案是200terms)
4. 用格仔紙畫下, 自己試下推理
收錄日期: 2021-05-01 15:57:11
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