1/1*3+1/3*5+1/5*7+.+1/2007*2009等于多少啊?
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 12:50:56
1/1*3+1/3*5+1/5*7+.+1/2007*2009等于多少啊?
1/1*3+1/3*5+1/5*7+.+1/2007*2009等于多少啊?
1/1*3+1/3*5+1/5*7+.+1/2007*2009等于多少啊?
1/1*3+1/3*5+1/5*7+.+1/2007*2009
=1/2(1-1/3+1/3-1/5+1/5-1/7+.1/2007-1/2009)
=1/2(1-1/2009)
=1/2 *2008/2009
=1004/2009
有人问过http://zhidao.baidu.com/question/109253354.html?si=3
裂项
原式=1/2(1-1/3+1/3-1/5+……+1/2007-1/2009)
=1004/2009
1/1*3+1/3*5+1/5*7+。。。+1/2007*2009
=0.5*(1-1/3 + 1/3-1/5 + 1/5-1/7 + …… +1/2007-1/2009)
=0.5*(1-1/2009)
=1004/2009
=1/2*(1/1-1/3)+1/2*(1/3-1/5)+...+1/2*(1/2007-1/2009)=1/2*(1-1/2009)=1004/2009
因为1/1*3=1/2*(1-1/3)
同理可得1/3*5=1/2(1/3-1/5)
这是用裂项法的
所以原式=
= 1/2(1-1/3+1/3-1/5+……+1/2007-1/2009)
= 1/2*(1-1/2009)
= 1004/2009
1-3+5-7+...
(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简算(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简便计算
1/1*3+1/1*3*5+1/1*3*5*7+1/1*3*5*7*9-73/945
(1/3+1/5+1/7)*(1/5+1/7+1/9)-(1/3+1/5+1/7+1/9)*(1/5+1/7)=?
1/3+1/5+1/7+.+1/2n+1
1/1*3*5+1/3*5*7+1/5*7*9.+1/95*97*99
1/1×3+1/3×5+1/5×7+1/7×9.+1/2011×2013
简算:1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19=
计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21)
1/1×3+1/3×5+1/5×7+1/7×9+.+1/2013×2015
1/1*3+1/3*5+1/5*7+1/7*9+.+1/101*103
帮帮忙1/1*3+1/3*5+1/5*7+1/7*9+...1/99*101
1/1*3+1/3*5+1/5*7+1/7*9+1/49*51=
计算:1/1×3+1/3×5+1/5×7+1/7×9``````+1/2001×2003
(1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1
1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
(1*3)/1+(3*5)/1+(5*7)/1+(7*9)/1+(9*11)/1