1/2+1/6+1/12+1/20+1/30+1/42+1/56+...+1/90求解答最好能讲解

1/2+1/6+1/12+1/20+1/30+1/42+1/56+...+1/90求解答最好能讲解
1/2+1/6+1/12+1/20+1/30+1/42+1/56+...+1/90求解答
最好能讲解

1/2+1/6+1/12+1/20+1/30+1/42+1/56+...+1/90求解答最好能讲解
1/2+1/6+1/12+1/20+1/30+1/42+1/56+...+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+.+1/9-1/10
=1-1/10
=9/10

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)＋(1/7－1/8)＋(1/8－1/9)＋(1/9－1/10)
＝1－1/10
＝9/10