1/1*3+1/3*5+1/5*7+.+1/99*101

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1/1*3+1/3*5+1/5*7+.+1/99*101
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1/1*3+1/3*5+1/5*7+.+1/99*101
1/1*3+1/3*5+1/5*7+.+1/99*101

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

1/1*3+1/3*5+1/5*7+。。。+1/99*101
=2×(1/1*3+1/3*5+1/5*7+。。。+1/99*101)÷2
=(2/1*3+2/3*5+2/5*7+......2/97*99+2/99*101)÷2
=(1-1/3+1/3-1/5+1/5-1/7+.......1/97-1/99+1/99-1/101)÷2
=(1-1/101)÷2
=100/101÷2
=50/101

答案是50/101,过程如下，观察分母的结构，可以看出分母是（2n-1）×（2n+1），n从1到50,
1/((2n-1)*(2n+1))=1/2(1/(2n-1)-1/(2n+1)),那么原式可以写成1/2(1-1/3+1/3-1/5+…+1/99-1/101)=1/2×100/101=50/101,这种因式分解的方法在数列的求和中经常用到，希望你能掌握

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