1/6+1/12+1/20+1/30+1/42+1/56+.+1/9900

来源：学生作业帮助网编辑：作业帮时间：2024/05/01 22:23:58

1/6+1/12+1/20+1/30+1/42+1/56+.+1/9900
1/6+1/12+1/20+1/30+1/42+1/56+.+1/9900

1/6+1/12+1/20+1/30+1/42+1/56+.+1/9900
1/6+1/12+1/20+1/30+1/42+1/56+...+1/9900
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+...+1/(99×100)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+...+1/99-1/100
=1/2-1/100
=49/100

1/6=1/2*(1/3)=1/2-1/3
所以1/2-1/3+1/3-1/4+...+1/99-1/100=1/2-1/100=49/100

=1/2×3+1/3×4+1/4×5+....+1/99×100
=1/2-1/3+1/3-1/4+...-1/99+1/99-1/100
=49/100