問題~
5該快d呀~!好急用
1. 1+2+3+4+...+300=? (45150)?
2. 1+4+7+10+13+...+301=? (15100)?
3. 50+51+52+53+...+100=? (3750)?
4. 200+199+198+197+...+0=? (200000)?
5. 50+40+30+20+...+(-200)=? (-1750)?
6. -52-54-56-58-...-200=? (-18900)?
7. -6-1+4+9+...+99=? (4836)?
8.111+555+999+...+4995=? (76590)?
9.11-12+13-14+15-16+...-300=? (-290)?
10.1"2-2"2+3"2-4"2+5"2-6"2+...-100"2=? (-1050)
"=次方
括號里面係計到既~5知岩5岩~
所有答案都要~
數學的問題??幫幫手
2008-11-07 3:41 am
回答 (2)
2008-11-07 7:57 am
✔ 最佳答案
1. (1+300)x 300 x 1/2 = 45150
2. (1+301)x[(301-1)/(4-1)+1]/2
= 15251
3. (50+100)x(100-50+1)/2
= 3825
4. (200+0)x201/2
= 20100
5. [50+(-200)]x[(-200-50)/(40-50)]/2
= -1875
6. [(-52)+(-200)]x[((-200)-(-52))/((-54)-(-52))+1]/2
= -9450
7. [(-6)+99]x[(99-(-6))/((-1)-(-6))+1]/2
=1023
8. 111+555+999+...+4995
= 111+111x5+111x9+...+111x45
= 111x(1+5+9+...+45)
= 111x(1+45)x[(45-1)/(5-1)+1]/2 = 30636
9. 11-12+13-14+15-16+...-300
= (11+13+15+...+299) - (12+14+16+...+300)
= (11+299)x[(299-11)/2+1]/2 - (12+300)x[(300-12)/2+1]/2 = -145
10. 1^2-2^2+3^2-4^2+...-100^2
= (1^2+2^2+3^2+4^2+...+100^2) - 2*(2^2+4^2+...+100^2)
= (1^2+2^2+3^2+4^2+...+100^2) - 8*(1^2+2^2+...+50^2)
= 100x101x201/6 - 8x50x51x101/6
= -5050
參考: myself
2008-11-07 6:01 am
等差數列之和=(首項+尾項)*項數/2
1. (1+300)*300/2 = 45150
2. (1+301)*[(301-1)/(4-1)+1]/2 = 15251
3. (50+100)*(100-50+1)/2 = 3825
4. (200+0)*201/2 = 20100
5. [50+(-200)]*[(-200-50)/(40-50)]/2 = -1875
6. [(-52)+(-200)]*[((-200)-(-52))/((-54)-(-52))+1]/2 = -9450
7. [(-6)+99]*[(99-(-6))/((-1)-(-6))+1]/2=1023
8. 111+555+999+...+4995
= 111+111*5+111*9+...+111*45
= 111*(1+5+9+...+45)
= 111*(1+45)*[(45-1)/(5-1)+1]/2 = 30636
9. 11-12+13-14+15-16+...-300
= (11+13+15+...+299) - (12+14+16+...+300)
= (11+299)*[(299-11)/2+1]/2 - (12+300)*[(300-12)/2+1]/2 = -145
公式: 1^2+2^2+...+n^2 = n*(n+1)*(2n+1)/6, n=1,2,3,...
10. 1^2-2^2+3^2-4^2+...-100^2
= (1^2+2^2+3^2+4^2+...+100^2) - 2*(2^2+4^2+...+100^2)
= (1^2+2^2+3^2+4^2+...+100^2) - 8*(1^2+2^2+...+50^2)
= 100*101*201/6 - 8*50*51*101/6
= -5050
1. (1+300)*300/2 = 45150
2. (1+301)*[(301-1)/(4-1)+1]/2 = 15251
3. (50+100)*(100-50+1)/2 = 3825
4. (200+0)*201/2 = 20100
5. [50+(-200)]*[(-200-50)/(40-50)]/2 = -1875
6. [(-52)+(-200)]*[((-200)-(-52))/((-54)-(-52))+1]/2 = -9450
7. [(-6)+99]*[(99-(-6))/((-1)-(-6))+1]/2=1023
8. 111+555+999+...+4995
= 111+111*5+111*9+...+111*45
= 111*(1+5+9+...+45)
= 111*(1+45)*[(45-1)/(5-1)+1]/2 = 30636
9. 11-12+13-14+15-16+...-300
= (11+13+15+...+299) - (12+14+16+...+300)
= (11+299)*[(299-11)/2+1]/2 - (12+300)*[(300-12)/2+1]/2 = -145
公式: 1^2+2^2+...+n^2 = n*(n+1)*(2n+1)/6, n=1,2,3,...
10. 1^2-2^2+3^2-4^2+...-100^2
= (1^2+2^2+3^2+4^2+...+100^2) - 2*(2^2+4^2+...+100^2)
= (1^2+2^2+3^2+4^2+...+100^2) - 8*(1^2+2^2+...+50^2)
= 100*101*201/6 - 8*50*51*101/6
= -5050
收錄日期: 2021-04-21 01:53:00
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081106000051KK01471