1+1⼀2-1⼀3+1⼀4-1⼀5+1⼀6-1⼀7+1⼀8-1⼀9+1⼀10-1⼀11+1⼀12 等于多少 要分数的答案 谢谢

原式=1+1/2+1/4+1/6+1/8+1/10+1/12
-1/3-1/7-1/9-1/11
=1+(6+3+2+1)/12+(5+4)/40
-(3+1)/9-(11+7)/77
=1+1+9/40-4/9-18/77
=9/40+5/9+59/77
=(9×9×77+5×40×77+59×40×5)/(360×77)
=33437/27720
=1+5717/27720

拆分每个分数。记住等式：1/(x(x+1))=1/x-1/(x+1)所以，原等式就可以简化为1/1-1/10=0.9

[image]20 1+1/2-1/3+1/4-1/5+1/6-1/7+1/8-1/9+1/10-1/11+1/12 =1+(1/2+1/4+1/8)-(1/3+1/9)-(1/5-1/10)+(1/6+1/12)-1/7-1/11
=1+7/8-4/9-1/10+1/4-(1/7+1/11)
=1+(7/8+1/4)-(4/9+1/10)-18/77
=1+9/8-49/90-18/77
=9/8-18/77+1-49/90
=549/616+41/90
=37333/27720