1/12+1/20+1/30+1/42+1/56+1/72= 等于多少?

题目

1/12+1/20+1/30+1/42+1/56+1/72= 等于多少?
求1/12+1/20+1/30+1/42+1/56+1/72= 等于多少,

答案

1/12+1/20+1/30+1/42+1/56+1/72
=1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/3-1/9
=2/9