计算：1除以1乘3+1除以2乘4+1除以3乘5.+1除以9乘11
问题描述：
计算：1除以1乘3+1除以2乘4+1除以3乘5.+1除以9乘11
答
易知1/n(n+2)=1/2(1/n-1/n+2)
代入上面可得(1+1/2-1/10-1/11)/2=36/55
答
1/1*3+1/2*4+1/3*5+1/4*6+……+1/9*11
=(1/1*3+1/3*5+...+1/9*11)+(1/2*4+1/4*6+...+1/8*10)
=(1/1-1/3+1/3-1/5+...+1/9-1/11)/2+(1/2-1/4+1/4-1/6+...+1/8-1/10)/2
=(1-1/11)/2+(1/2-1/10)/2
=10/11*1/2+4/10*1/2
=5/11+1/5
=36/55