1/2+1/6+1/12+1/20+1/30+.+1/110=?

来源：学生作业帮助网编辑：六六作业网时间：2024/05/13 15:32:01

1/2+1/6+1/12+1/20+1/30+.+1/110=?1/2+1/6+1/12+1/20+1/30+.+1/110=?1/2+1/6+1/12+1/20+1/30+.+1/110=?1/2+

1/2+1/6+1/12+1/20+1/30+.+1/110=?
1/2+1/6+1/12+1/20+1/30+.+1/110=?

1/2+1/6+1/12+1/20+1/30+.+1/110=?
1/2+1/6+1/12+1/20+1/30+.+1/110
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/10-1/11
=1-1/11
=10/11

1/2+1/6+1/12+1/20+1/30+....+1/110
=1/2+1/(2*3)+1/(3*4)+1/(4*5)+......+1/(10*11)
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/10-1/11)
=1-1/11
=10/11

109/110

1/2+1/6+1/12+1/20+1/30+...+1/110
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...1/9-1/10+1/10-1/11
=1-1/11=10/11