1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11
问题描述：
1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11
答
先列一个通式吧
1/[n(n+2)]=0.5*[1/n -1/(n+2)]
所以原式可以化成
0.5*(1/2-1/4+1/3-1/5+1/4-1/6.........+1/9-1/11)=
0.5*[(1/2+1/3+1/4+1/5+...+1/9)-(1/4+1/5...+1/11)=
0.5*(1/2+1/3-1/10-1/11)=0.5*106/165=53/165
所以原式=53/165
答
1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11
=(1/2x4+1/4x6+1/6x8+1/8x10)+(13x5+1/5x7+1/7x9+1/9x11)
=(1/2)[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)]+(1/2[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=(1/2)(1/2-1/10)+(1/2)(1/3-1/11)
=1/5+4/33
=53/165