早教吧作业答案频道 -->数学-->
1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）=?
题目详情
1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）=?
▼优质解答
答案和解析
1/1*3+1/3*5+1/5*7+..+1/（2n+1）（2n+3）
=(1/2) * { (1-1/3)+(1/3-1/5)+(1/5-1/7)+……+ [ 1/(2n+1)-1/(2n+3) ] }
=(1/2) * { 1-1/3+1/3-1/5+1/5-1/7+……+1/(2n+1)-1/(2n+3) }
=(1/2) * { 1-1/(2n+3) }
=(1/2) * (2n+2)/(2n+3)
=(n+1)/(2n+3)
=(1/2) * { (1-1/3)+(1/3-1/5)+(1/5-1/7)+……+ [ 1/(2n+1)-1/(2n+3) ] }
=(1/2) * { 1-1/3+1/3-1/5+1/5-1/7+……+1/(2n+1)-1/(2n+3) }
=(1/2) * { 1-1/(2n+3) }
=(1/2) * (2n+2)/(2n+3)
=(n+1)/(2n+3)
看了 1/1*3+1/3*5+1/...的网友还看了以下：