問題:1+2+3+4.......100=??

👨🏻‍🏫 學術台數學

A0201773

2008-10-07 6:34 am

1+2+3.........100=????????

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更新1:

1+2+3.........200=??

更新2:

1+2+3......1000=?????

回答 (6)

[匿名]

2008-10-16 6:52 am

1+99=100 2+98=100................49+51=100 =5050
1+199=200.......................99+101=200 =10100
1+999=1000........................499+501=1000 =500500
I WISH I CAN HELP YOU!請選我做the best!plspls

參考: me and my maths teacher

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K K

2008-10-13 2:42 am

(1)1+99=100 2+98=100...........49+51=100 =5050
(2)1+199=200..................99+101=200 =10100
(3)1+999=1000.....................499+501=1000 =500500

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fighting gravity

2008-10-07 7:53 am

1+2+3....+100
=100*(1+100)/2
=100*1001/2
=100100/2
=5050

1+2+3....+200
=200*(1+200)/2
=200*201/2
=40200/2
=40100

1+2+3....+1000
=1000*(1+1000)/2
=1000*1001/2
=1001000/2
=50500

參考: me

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ngai

2008-10-07 6:44 am

1+2+3........+100
=(100/2)(100+1)
=5050

or
1+2+3........+100
=(1+100)/2 *100
5050

呢D係三角形數
頭+尾除2乘尾

2008-10-12 20:01:17 補充：
1+2+3+...+200
= 1+200+2+199+3+198+...+100+101
= 201 x 100
= 20100

1+2+3+...+1000
= 1+1000+2+999+3+998+...+500+501
= 1001 x 500
= 500500

參考: book

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lam099

2008-10-07 6:41 am

(頭+尾)X項數/2
(1+100)X100/2
=5050

參考: ME

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jaycelai1995

2008-10-07 6:39 am

(頭+尾)X 中間
= (1+100)X 50
=5050

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