问一道预备班的题目1-1/3=1/3×2,1/3-1/5=1/3×1/5×2,1/5-1/7=1/5×1/7×2,1/7-1/9=1/7×1/9×2,…请运用上面发现的规律计算下式的值1/1×3+1/3×5+1/5×7+1/9×11+1/11×13+1/13×15+1/15×17+1/17×19+1/19×21

Question

问一道预备班的题目
1-1/3=1/3×2,1/3-1/5=1/3×1/5×2,1/5-1/7=1/5×1/7×2,1/7-1/9=1/7×1/9×2,…
请运用上面发现的规律计算下式的值
1/1×3+1/3×5+1/5×7+1/9×11+1/11×13+1/13×15+1/15×17+1/17×19+1/19×21

Answer 1

1/1×3+1/3×5+1/5×7+1/7×9+1/9×11+1/11×13+1/13×15+1/15×17+1/17×19+1/19×21=1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15+1/15-1/17+1/17-1/19+1/19-1/21)=1/2×(1-1/21)=10/21