1 1 1 1 1 1 ____ + _____ + -------- + -------- + --------- + ----------- 1乘3乘5 3乘5乘7 5乘7乘9 71 1 1 1 1 1____ + _____ + -------- +
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![1 1 1 1 1 1 ____ + _____ + -------- + -------- + --------- + ----------- 1乘3乘5 3乘5乘7 5乘7乘9 71 1 1 1 1 1____ + _____ + -------- +](/uploads/image/z/1975751-71-1.jpg?t=1+1+1+1+1+1+____+%2B+_____+%2B+--------+%2B+--------+%2B+---------+%2B+-----------+1%E4%B9%983%E4%B9%985+3%E4%B9%985%E4%B9%987+5%E4%B9%987%E4%B9%989+71++++++++++++++++++1++++++++++++++++++++++++1++++++++++++++++++1+++++++++++++++++1+++++++++++++++++1____++++++%2B+++++_____+++++++++%2B+++--------++%2B)
1 1 1 1 1 1 ____ + _____ + -------- + -------- + --------- + ----------- 1乘3乘5 3乘5乘7 5乘7乘9 71 1 1 1 1 1____ + _____ + -------- +
1 1 1 1 1 1 ____ + _____ + -------- + -------- + --------- + ----------- 1乘3乘5 3乘5乘7 5乘7乘9 7
1 1 1 1 1 1
____ + _____ + -------- + -------- + --------- + -----------
1乘3乘5 3乘5乘7 5乘7乘9 7乘9乘11 9乘11乘13 11乘13乘15
1 1 1 1 1 1 ____ + _____ + -------- + -------- + --------- + ----------- 1乘3乘5 3乘5乘7 5乘7乘9 71 1 1 1 1 1____ + _____ + -------- +
1/(1×3×5)=1/4×[1/(1×3)-1/(3×5)]
1/(3×5×7)=1/4×[1/(3×5)-1/(5×7)]
1/(5×7×9)=1/4×[1/(5×7)-1/(7×9)]
1/(7×9×11)=1/4×[1/(7×9)-1/(9×11)]
1/(9×11×13)=1/4×[1/(9×11)-1/(11×13)]
1/(11×13×15)=1/4×[1/(11×13)-1/(13×15)]
提取公因式1/4,然后相互抵消,得原式=1/4×[1/(1×3)-1/(13×15)]=1/4×64/195=16/195