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计算:1/56+1/72+1/90+1/110+1/132+1/156+1/182=?
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计算:1/56+1/72+1/90+1/110+1/132+1/156+1/182=?
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答案和解析
1/56+1/72+1/90+1/110+1/132+1/156+1/182=?
1/(7*8)+1/(8*9)+1/(9*10)+1/(11*10)+1/(11*12)+1/(12*13)+1/(13*14)
=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13+1/13-1/14
=1/7-1/14
=1/14
1/(7*8)+1/(8*9)+1/(9*10)+1/(11*10)+1/(11*12)+1/(12*13)+1/(13*14)
=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13+1/13-1/14
=1/7-1/14
=1/14
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