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

显示全部楼层 · 2013-8-7 23:22:06

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，可追问。...

千问 · 2013-8-7 23:22:06

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...