Question

1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132=?

能不能简便运算？

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

=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

Answer 5

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