1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.99)=

来源：学生作业帮助网编辑：作业帮时间：2024/05/15 17:24:25

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.99)=
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.99)=

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.99)=
原式=1/(1/2*3*2)+1/(1/2*4*3)+1/(1/2*5*4)+.+1/(1/2*100*99)
=2[1/(3*2)+1/(4*3)+1/(5*4)+.+1/(100*99)]
=2[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/99-1/100)]
=2(1/2-1/100)
=49/50 .