1/13+1/35+1/37+...+1/99101

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

1/1*3+1/3*5+1/3*7+...+1/99*101
=1/2(2/1*3+2/3*5+2/5*7+……+2/99*101)
=1/2(1-1/3+1/3-1/5+1/5-……-1/99+1/99-1/101)
=1/2(1-1/101)
=50/101
看其中的一个如2/31*33=(33-31)/31*33=1/31-1/33

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你的题目有点问题啊！应该是1/1*3+1/3*5+1/5*7+1/7*9+......1/99*101吧！这是个
很简单的数学题而且很经典以后可能经常考一定要记住了啊
1/1*3=(1/2)*(1/1-1/3);
1/3*5=(1/2)*(1/3-1/5);
1/5*7=（1/2)*(1/5-1/7);
.
.
1/99*101=(1/2)*(1/99-1/101)
以上各式左边与左边相加右边与右边相加得
1/1*3+1/3*5+1/5*7+......1/99*101=(1/2)*(1/1-1/3+1/3-1/5+1/5-1/7+......+1/97-1/99+1/99-1/101)
=（1/2)*(1-1/101)
=50/101

收起

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

1/1*3+1/3*5+1/5*7+......1/99*101=(1/2)*(1/1-1/3+1/3-1/5+1/5-1/7+......+1/97-1/99+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+.+1/2n+1 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 1/1*3+1/3*5+1/5*7+1/7*9+.+1/49*51 1/1*3+1/3*5+1/5*7+1/7*9+...+1/2007*2009=?