1×3分之1加上3×5分之一加5×7分之一加7×9分之一加9×11,怎么计算,
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用裂项法：
1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
= (1/2)×(1-1/3)+(1/2)×(1/3-1/5)+(1/2)×(1/5-1/7)+(1/2)×(1/7-1/9)+(1/2)×(1/9-1/11)
= (1/2)×[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
= (1/2)×(1-1/11)
= 5/11
1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)
= (1/2)×(1-1/3)+(1/2)×(1/3-1/5)+(1/2)×(1/5-1/7)+(1/2)×(1/7-1/9)+(1/2)×(1/9-1/11)
= (1/2)×[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
= (1/2)×(1-1/11)
= 5/11
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