1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?能不能简便运算?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/09 06:31:55
1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?能不能简便运算?1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?能不能简便运

1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?能不能简便运算?
1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?
能不能简便运算?

1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?能不能简便运算?
1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+……+1/11-1/12
=1/4-1/12
=3/12-1/12
=2/12
=1/6

1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/5-1/6+1/6-1/7+1/7-1/8+……+1/11-1/12
=1/5-1/12
=7/60

1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/5-1/6+1/6-1/7+1/7-1/8+……+1/11-1/12
=1/5-1/12
=7/60

1/20=1/4-1/5
1/30=1/5-1/6
......
1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=1/4-1/12=1/6

=1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11)+1/(11*12)=1/4-1/5+1/5-1/6+~~~~~+1/10-1/11+1/11-1/12=1/4-1/12=1/6