1／1×3+1／3×5+1／5×7+.+1／99×101怎么做救急救急!我的作业没写完,快开学了,

来源：学生作业帮助网编辑：作业帮时间：2024/11/08 20:01:57

1／1×3+1／3×5+1／5×7+.+1／99×101怎么做救急救急!我的作业没写完,快开学了,
1／1×3+1／3×5+1／5×7+.+1／99×101怎么做
救急救急!我的作业没写完,快开学了,

1／1×3+1／3×5+1／5×7+.+1／99×101怎么做救急救急!我的作业没写完,快开学了,
1／1×3+1／3×5+1／5×7+.+1／99×101
=(2／1×3+2／3×5+2／5×7+.+2／99×101)/2
=[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)]/2
=(1-1/101)/2
=50/101

原式=1/2*(1/1-1/3+1/5-1/7+...-1/99+1/99-1/101)
=1/2*(1-1/101)
=100/202
=50/101

用裂项相消

1／1×3+1／3×5+1／5×7+......+1／99×101
=1/2(1-1/3+1/3-1/5+……+1/99-1/101)
=1/2(1-1/101)
=1/2*(100/101)
=50/101

因为：
1／1×3=1/2(2／1×3)=1/2(1/1-1/3)
1／3×5=1/2(2／3×5)=1/2(1/3-1/5)
……
1／1×3+1／3×5+1／5×7+......+1／99×101
＝1/2[(1/1-1/3+1/3-1/5+……+1/99-1/101)]
＝1/2(1-1/101)=50/101

原式＝(1/2)(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=(1/2)(1-1/101)
=50/101

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