1/30+1/42+1/56+1/72=
4个回答

原式=1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)

=(6-5)/(5×6)+(7-6)/(6×7)+(8-7)/(7×8)+(9-8)/(8×9)

=6/(5×6)-5/(5×6)+7/(6×7)-6/(6×7)+8/(7×8)-7/(7×8)+9/(8×9)-8/(8×9)

=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9

=1/5-1/9

=9/45-5/45

=4/45