简便计算(1)2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13

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简便计算(1)2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13
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简便计算(1)2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13
简便计算(1)2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13

简便计算(1)2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13
2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13
=1-1/13
=12/13

2/3=2/1×3=(1-1/3)
2/(3×5)=(1/3-1/5)
……
2/11×13=1/11-1/13
所以2/3+2/3×5+2/5×7+2/7×9+2/9×11+2/11×13
=1-1/3+1/3-1/5+……+1/11-1/13
=1-1/13
=12/13