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(1%1/2%1/3%1/4%1/5)(1/2+1/3+1/4+1/5+1/6)%(...

原式=(1-1/2-1/3-1/4-1/5)*(1/2+1/3+1/4+1/5)+1/6*(1-1/2-1/3-1/4-1/5) -(1-1/2-1/3-1/4-1/5)*(1/2+1/3+1/4+1/5)+1/6*(1/2+1/3+1/4+1/5) =1/6*(1-1/2-1/3-1/4-1/5+1/2+1/3+1/4+1/5) =1/6*1 =1/6

设(1-1/2-1/3-1/4-1/5)=X;(1/2+1/3+1/4+1/5)=Y; 原式=X*(Y+1/6)-(X-1/6)Y=XY+X*1/6-XY+Y*1/6=1/6*(X+Y)=1/6*1=1/6

设(1-1/2-1/3-1/4-1/5)为a,(1/2+1/3+1/4+1/5)为b,代入得转化为a(b+1/6)-(a-1/6)b,得到ab+1/6a-ab+1/6b,化简为1/6(a+b),再重新代入,解得1/6(1-1/2-1/3-1/4-1/5+1/2+1/3+1/4+1/5)=1/6*1=1/6

(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20) =1/2(1+1/2+1/3+1/4)-1/3(1+1/2+1/3+1/4)+1/4(1+1/2+1/3+1/4)-1/5(1+1/2+1/3+1/4) =(1+1/2+1/3+1/4)(1/2-1/3+1/4-1/5) =(12+6+4+3)/12*(30-20+15-12)/6...

设+1/2+1/3+1/4=x 1/2+1/3+1/4+1/5=y (1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4) =(1+x)y-(1+y)x =y+xy-x-xy =y-x =1/5

1*1/2+1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/51/5-1/6+1/6-1/7 =1-1/7 =6/7 (此题的关键是要知道N分之一乘N减1分之一,等于N分之一减N减1分之一。)

(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

当n很大时,有:1+1/2+1/3+1/4+1/5+1/6+...1/n = 0.57721566490153286060651209 + ln(n)//C++里面用log(n),pascal里面用ln(n) 0.57721566490153286060651209叫做欧拉常数 to GXQ: 假设;s(n)=1+1/2+1/3+1/4+..1/n 当 n很大时 sqrt(n+1) = sqrt(n...

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