1+ 1+2分之一+1+2+3分之一....1+2+3....+10分之一

显示全部楼层 · 2010-7-25 13:47:14

需要简便方法谢谢！

千问 · 2010-7-25 13:47:14

1/(1+2+...+n) = 2/(n)(n+1) = 2[1/n - 1/(n+1)]1+1/(1+2)+1/(1+2+3)+....+1/(1+2+3+...+10)=2 (1/1-1/2)+2(1/2-1/3)+2(1/3-1/4) + ...+2(1/10-1/11)=2(1-1/2+1/2-1/3+1/3-1/4+....+1/10-1/11) =2(1-1/11)=2*10/11=20/11

千问 · 2010-7-25 13:47:14

原式=(2/(1*2))+(2/(2*3))+(2/(3*4))+...+(2/(10*11))=2[(1/(1*2))+(1/(2*3))+(1/(3*4))+...+(1/(10*11))=2[1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/10)-(1/11)]=2[1-(1/11)]=2*10/11=