问题标题:
简便方法解:41*3-83*5+125*7-167*9+209*11-2411*13""是表示分数,如41*3是1*3分之4
问题描述:
简便方法解:41*3-83*5+125*7-167*9+209*11-2411*13
""是表示分数,如41*3是1*3分之4
孙世魁回答:
41*3-83*5+125*7-167*9+209*11-2411*13
=(1+3)/(1×3)-(3+5)/(3×5)+(5+7)/(5×7)-(7+9)/(7×9)+(9+11)/(9×11)-(11+13)/(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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