计算2/2²-1+2/4²-1+2/6²-1+2/8²-1+2/10²

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/16 17:06:16

计算2/2²-1+2/4²-1+2/6²-1+2/8²-1+2/10²-1+2/12²-1.
要有算式和答案

2/(2²-1)+2/(4²-1)+2/(6²-1)+2/(8²-1)+2/(10²-1)+2/(12²-1)
=2/[(2-1)×(2+1)]+2/[(4-1)×(4+1)]+2/[(6-1)×(6+1)]+2/[(8-1)×(8+1)]+2/[(10-1)×(10+1)]+2/[(12-1)×(12+1)]
=2/(1×3)+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)
=1-1/3+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
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