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(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)%(1+1/2+1/3+1/4+

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

原式=(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)×(1/2+1/3+1/4)-(1/5)×(1/2+1/3+1/4)=(1+1/2+1/3+1/4)×(1/5)-(1/5)×(1/2+1/3+1/4)=(1/5)×1=1/5 原式=1/2+(1/3+2/3)+(1/4+2/4+3/4)+……+(1/10+2/10+3/10+…+9/10)=1/2+1+3/2+2+5/2+3+7/2+4+...

a=1/2+1/3+1/4=13/12 (1+a)*a-(a+(1/5))*a =(4/5)*a =13/15

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

原式 =1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55 =2×(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110) =2×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11) =2×(1-1/11) =2×10/11 =20/11 公式: 1+...

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...

利用“欧拉公式” ,1+1/2+1/3+……+1/n =ln(n)+C,(C为欧拉常数) ,所以没有具体值。欧拉常数近似值约为0.57721566490153286060651209 在微积分学中,欧拉常数γ有许多应用,如求某些数列的极限,某些收敛数项级数的和等.例如求lim[1/(n+1)+1/(n+2)+…+1...

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...

(1+1/2+1/3+1/4)*(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)*(1/2+1/3+1/4) =(1/2+1/3+1/4)*[(1+1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)] =(1/2+1/3+1/4)*(1-1/5) =(1/2+1/3+1/4)*4/5 =13/12 * 4/5 =13/15

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

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