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1/2+1/(2+3)+1/(2+3+4)+1/(2+3+4+5)+...+1/...

把分子写成分母的最大数减1 ,得 原式=(2-1)/(1*2)+(3-1)/(1*2*3)+(4-1)/(1*2*3*4)+(5-1)/(1*2*3*4*5) =[2/(1*2)-1/(1*2)]+[3/(1*2*3)-1/(1*2*3)]+[4/(1*2*3*4)-1/(1*2*3*4)]+[5/(1*2*3*4*5)-1/(1*2*3*4*5)] =[1/1-1/(1*2)]+[1/(1*2)-1/(1*2*3)]...

分数裂项: 先按等差数列公式计算: 1/2=2/1*4 1/(2+3)=2/2*5 1/(2+3+4)=2/3*6 …… 1/(2+3+...+200)=2/199*202 再按公式裂项: 2/1*4=(1-1/4)*2/3 2/2*5=(1/2-1/5)*2/3 …… 2/199*202=(1/199-1/202)*2/3 原式=(1+1/2+1/3-1/200-1/201...

1/2+(1/3+2/3)+(1/4+2/4+3/4)+……(1/50+2/50+…+48/50+49/50)= 先总结一下,凡是分母是奇数的,如(1/3+2/3)=1 (1/5+2/5+3/5+4/5)=2,都是整数,且等于(奇数-1)/2 以此类推,(1/49+2/49+…+48/49)= 24 分母是偶数的,如1/2=0.5,(1/4+2/4+3/4)=1.5...

(1/2+1/3+1/4+……+1/99+1/100)+(2/3+2/4+2/5+……+2/99+2/100)+……+(98/99+98/100)+99/100) =1/2+(1/3+2/3)+(1/4+2/4+3/4)+……(1/100+2/100+3/100+……+99/100) =1/2+2/2+3/2+……+99/2 =(1/2+99/2)×99/2 =50×99/2 =2475

2/1+(-3/2)-(-5/4)+(-2/1) =2分之1-2分之1-3分之2+5分之4 =-15分之10+15分之12 =15分之2

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