作业帮1/2+1/6+1/12+1/20+1/30+.+1/110=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/14 14:45:14
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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