计算:1/1乘以3+1/2乘以4+1/3乘以5+...+1/9乘以11
问题描述：
计算:1/1乘以3+1/2乘以4+1/3乘以5+...+1/9乘以11
答
设A=1/1×3+1/2×4+1/3×5+...+1/9×11
则2A=2/1×3+2/2×4+2/3×5+...+2/9×11
=(3-1)/1×3+(4-2)/2×4+(5-3)/3×5+...+(11-9)/9×11
=1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11
=1+1/2-1/10-1/11
=309/220.
答
1/1乘以3+1/2乘以4+1/3乘以5+...+1/9乘以11
=(1-1/3+1/2-1/4+1/3-1/5+……+1/9-1/11）/2
=（1+1/2-1/10-1/11）/2
=36/55