2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11 简便计算

2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11 简便计算
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11 简便计算

2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11 简便计算
1/1×3=(1-1/3)/2
1/3×5=(1/3-1/5)/2
1/5×7=(1/5-1/7)/2
.
.
1/9×11=(1/9-1/11)/2
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11
=2002×1/2×(1/1×3+1/3×5+1/5×7+1/7×9+1/9×11)
=2002×1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=2002×1/2×(1-1/11)
=2002×1/2×10/11
=910

1/1×3=（1-1/3）/2
1/3×5=（1/3-1/5）/2
1/5×7=（1/5-1/7）/2
.
.
1/9×11=（1/9-1/11）/2
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11
=2002*（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）/2
=2002*（10/11）/2
=910

1/(1×3)=(1-1/3)*0.5
1/(3×5)=(1/3-1/5)*0.5
1/(5×7)=(1/5-1/7)*0.5
1/(7×9)=(1/7-1/9)*0.5
1/(9×11)=(1/9-1/11)*0.5
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11
=2002×【1/(1×3)+1/(3×...

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1/(1×3)=(1-1/3)*0.5
1/(3×5)=(1/3-1/5)*0.5
1/(5×7)=(1/5-1/7)*0.5
1/(7×9)=(1/7-1/9)*0.5
1/(9×11)=(1/9-1/11)*0.5
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11
=2002×【1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)】
=2002×【(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)*0.5】
=2002×(1-1/11)*0.5
=2002×10/11*0.5
=1820 *0.5
=910

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