1/1*3+1/3*5+1/5*7+...+1/99*101=?(要简便)

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1/1*3+1/3*5+1/5*7+...+1/99*101=?(要简便)

1/1*3+1/3*5+1/5*7+...+1/99*101=?(要简便)
1/1*3+1/3*5+1/5*7+...+1/99*101=?(要简便)

1/1*3+1/3*5+1/5*7+...+1/99*101=?(要简便)
1/1*3+1/3*5+1/5*7+...+1/99*101
=(1-1/3)÷2+(1/3-1/5)÷2+(1/5-1/7)÷2+……+(1/99-1/101)÷2
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)]÷2
=(1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)÷2
中间互相抵消
=(1-1/101)÷2
=100/101÷2
=50/101

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

利用公式1/(n)(n+2)=1/2[1/n-1/(n+2)]
1/3*1+1/3*5+1/5*7+...+1/99*101
=1/2（1-1/3）+1/2（1/3-1/5）……1/2(1/99-1/101)
=1/2(1-1/3+1/3-1/5……1/99-1/101)
=1/2（1-1/101）
=1/2*100/101
=55/101

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