1/2+(1/3+2/3)+(1/4+2/4+3/4)+···+(1/10+2/10+···9/10)还有这道(1+1/2)*(1+1/4)*(1+1/6)*···*(1+1/10)*(1-1/3)*(1-1/5)*···*(1-1/9)
问题描述:
1/2+(1/3+2/3)+(1/4+2/4+3/4)+···+(1/10+2/10+···9/10)
还有这道(1+1/2)*(1+1/4)*(1+1/6)*···*(1+1/10)*(1-1/3)*(1-1/5)*···*(1-1/9)
答
计算每一项:1/k+2/k+..+(k-1)/k=1/k*[1+2+..+(k-1)]=1/k*k(k-1)/2=(k-1)/2所以1/2+(1/3+2/3)+(1/4+2/4+3/4)+···+(1/10+2/10+···9/10)=1/2+2/2+3/2+..+9/2=1/2*(1+2+..+9)=1/2*9*10/2=45/2(1+1/2)*(1+1...