1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19=

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/19 12:14:44
1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19=

1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19=
1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19=

1/1*3+1/3*5+1/5*7+1/7*9+...1/17*19=
9/19

=(1-1/3+1/3-1/5+1/5-1/7+...+1/17-1/19)/2
=(1-1/19)/2
=9/19

原式=1/2（1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9.....+1/17-1/19）=1/2×（1-1/19）=9/19

因1-1/3=2/1*3.则1/1*3=1/2(1-1/3),同理：1/3*5=1/2(1/3-1/5),1/5*7=1/2(1/5-1/7),......1/17*19=1/2(1/17-1/19).所以：原式=1/2(1-1/3+1/3-1/5+1/5-.......-1/19)=1/2*18/19=9/19

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+.+1/2n+1 (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 1 1 1 1 3 5 7 1 5 13 25 1 7 25 why 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