已知5/6=1/2+1/3,7/12=1/3+1/4,9/20=1/4+1/5······计算:1+1/2-5/6+7/12-9/20+11/30-13/42

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 04:10:57
已知5/6=1/2+1/3,7/12=1/3+1/4,9/20=1/4+1/5······计算:1+1/2-5/6+7/12-9/20+11/30-13/42

已知5/6=1/2+1/3,7/12=1/3+1/4,9/20=1/4+1/5······计算:1+1/2-5/6+7/12-9/20+11/30-13/42
已知5/6=1/2+1/3,7/12=1/3+1/4,9/20=1/4+1/5······
计算:1+1/2-5/6+7/12-9/20+11/30-13/42

已知5/6=1/2+1/3,7/12=1/3+1/4,9/20=1/4+1/5······计算:1+1/2-5/6+7/12-9/20+11/30-13/42
1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7
=1-1/7
=6/7

原式=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)
=1-1/7
=6/7