数学题 1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2007*2009)
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/28 05:57:45
数学题 1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2007*2009)
数学题 1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2007*2009)
数学题 1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2007*2009)
1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2007*2009)
=1-1/3+1/3-1/5+1/5-1/7+...+1/2007-1/2009
=1-1/2009
=2008/2009
原式=1/2〔1-1/3〕+1/2〔1/3-1/5〕+...+1/2〔1/2007-1/2009〕
=1/2〔1-1/2009〕
=1/2*2008/2009
=1004/2009