吾識做數學功課...(中一級的)

Akari

2013-06-24 11:17 pm

吾識做數學功課,請教教我...(要列式!)
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.I enter an elevator at the 30th floor of a building.The elevator first ascends 15
levels and then descends 37 levels before I leave the elevator.Using positive and
negative numbers to represent the up and down of the elevator respectively,what
is the overall change in the position of the elevator?

謝謝!(^^)

回答 (1)

Tony

2013-06-24 11:41 pm

✔ 最佳答案

1. (+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)
Is there mistyping error on +1?Is it -1?
If it is(-1)+(-2)+(+3)+(-4)+...+(+99)+(-100),
you can group numbers as -100 by each two numbers
(-1)+(-99) = -100
(-2)+(-98) = -100 and so on untill
(-49)+(-51)= -100
(-50 cannot be grouped like above)
(-1)+(-2)+(+3)+(-4)+...+(+99)+(-100)
= 49(-100)+(-50)+(-100)
= 50(-100)+(-50)
= -5050
If it is (+1)+(-2)+(+3)+(-4)+...+(+99)+(-100),
(+1)+(-2)+(+3)+(-4)+...+(+99)+(-100)
= (-1)+(-2)+(+3)+(-4)+...+(+99)+(-100)+2
= -5050+2
= -5048

2. ascends 15 levels= +15, descends 37 levels= -37
overall change = +15-37 = -22
the elevator descends 22 levels
new position = 30-22=8th floor

參考: myself

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