1/1*3+1/2*4+1/3*5+……+1/9*11怎么算~(>_

1/1*3+1/2*4+1/3*5+……+1/9*11怎么算~(>_
1/1*3+1/2*4+1/3*5+……+1/9*11怎么算~(>_

1/1*3+1/2*4+1/3*5+……+1/9*11怎么算~(>_
数列求和：
1/1*2*3+1/2*3*4+...+1/n(n+1)(n+2)
=1/2(1/1*2-1/2*3+1/2*3-1/3*4+.+1/n(n+1)-1/(n+1)(n+2))
=1/2*(1/2-1/(n+1)(n+2))=1/4-1/2(n+1)(n+2)
1/1*3+1/2*4+1/3*5+...+1/9*11
=1/2*(1-1/3+1/2-1/4+1/3-1/5+...+1/8-1/10+1/9-1/11)
=1/2*(1+1/2-1/10-1/11)
=1/2*72/55
=36/55
如果不清楚,

裂项相消啊
1/1*3+1/2*4+1/3*5+……+1/9*11
=1/2（1-1/3+1/2-1/4.......+1/8-1/10+1/9-1/11）
=1/2（1+1/2-1/10-1/11）
=41/55