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數學的問題??幫幫手
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=? ... 顯示更多 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~
最佳解答:
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
其他解答:
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
數學的問題??幫幫手
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發問: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=? ... 顯示更多 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~
最佳解答:
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
其他解答:
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
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