1/11×13×15+1/13×15×17+······+1/29×31×33
题目
1/11×13×15+1/13×15×17+······+1/29×31×33
答案
由1/[(2n-1)(2n+1)(2n+3)]={1/[2n-1)(2n+1)]-1/(2n+1)(2n+3)]}/4
1/(11×13×15)+1/(13×15×17)+……+1/(29×31×33)
=1/4{[1/(11×13)-1/(13×15)]+[1/(13×15)-1/(15×17)]+……+[1/(29×31)-1/(31×33)]}
=1/4{1/(11×13-1/(31×33)}
=20/(13×31×33)=20/13299
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