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1.(%1/3)%(%1/2)+3/4+(%2/3) 2.1.36%(%2.64+5.2)%0...

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...

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...

1/1*2*3+1/2*3*4+……1/n(n+1)(n+2) =1/2(1/1*2-1/2*3)+1/2(1/2*3-1/3*4)+...+1/2[1/n(n+1)-1/(n+1)(n+2)] =1/2[1/1*2-1/2*3+1/2*3-1/3*4+...+1/n(n+1)-1/(n+1)(n+2)] =1/2[1/1*2-1/(n+1)(n+2)] =1/2*[(n+1)(n+2)-2]/2(n+1)(n+2) =(n^2+3n)/4(n+1)...

=[(1/2+1/3+......+1/2002)*(1/2+1/3+1/4+......+1/2003) +(1/2+1/3+1/4+......+1/2003)] -[(1/2+1/3+1/4+.....

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