计算:1/2+1/6+1/12+1/20+1/30+...+1/(2010*2011)+1/(2011*2012)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 01:21:30

计算:1/2+1/6+1/12+1/20+1/30+...+1/(2010*2011)+1/(2011*2012)
计算:1/2+1/6+1/12+1/20+1/30+...+1/(2010*2011)+1/(2011*2012)

计算:1/2+1/6+1/12+1/20+1/30+...+1/(2010*2011)+1/(2011*2012)
1/2+1/6+1/12+1/20+1/30+...+1/(2010*2011)+1/(2011*2012)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2010-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012