作业帮2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?为什么这么做?2005/1×3+2005/3×5+2005/5×7+.+2005/99×1012005/(1×3)+2005/(3×5)+2005/(5×7)+……+2005/(99×101)=2005×[1/(1×3)+1/(3×5)+1/(5×7)+……+1/(99×101)]=2005×(1/2)×(1-1/3+1/3-1/5+1
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/11 14:05:21
![2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?为什么这么做?2005/1×3+2005/3×5+2005/5×7+.+2005/99×1012005/(1×3)+2005/(3×5)+2005/(5×7)+……+2005/(99×101)=2005×[1/(1×3)+1/(3×5)+1/(5×7)+……+1/(99×101)]=2005×(1/2)×(1-1/3+1/3-1/5+1](/uploads/image/z/67851-27-1.jpg?t=2005%2F1%2A3%2B2005%2F3%2A5%2B2005%2F5%2A7%2B%C2%B7%C2%B7%C2%B72005%2F99%2A101%3D%3F%E4%B8%BA%E4%BB%80%E4%B9%88%E8%BF%99%E4%B9%88%E5%81%9A%3F2005%2F1%C3%973%2B2005%2F3%C3%975%2B2005%2F5%C3%977%2B.%2B2005%2F99%C3%971012005%2F%281%C3%973%29%2B2005%2F%283%C3%975%29%2B2005%2F%285%C3%977%29%2B%E2%80%A6%E2%80%A6%2B2005%2F%2899%C3%97101%29%3D2005%C3%97%5B1%2F%281%C3%973%29%2B1%2F%283%C3%975%29%2B1%2F%285%C3%977%29%2B%E2%80%A6%E2%80%A6%2B1%2F%2899%C3%97101%29%5D%3D2005%C3%97%281%2F2%29%C3%97%281-1%2F3%2B1%2F3-1%2F5%2B1)
2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?为什么这么做?2005/1×3+2005/3×5+2005/5×7+.+2005/99×1012005/(1×3)+2005/(3×5)+2005/(5×7)+……+2005/(99×101)=2005×[1/(1×3)+1/(3×5)+1/(5×7)+……+1/(99×101)]=2005×(1/2)×(1-1/3+1/3-1/5+1
2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?为什么这么做?
2005/1×3+2005/3×5+2005/5×7+.+2005/99×101
2005/(1×3)+2005/(3×5)+2005/(5×7)+……+2005/(99×101)
=2005×[1/(1×3)+1/(3×5)+1/(5×7)+……+1/(99×101)]
=2005×(1/2)×(1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)
=2005×(1/2)×(1-1/101)
=2005×(1/2)×(100/101)
=2005×(50/101)
=100250/101
为什么这么做?
2005/1*3+2005/3*5+2005/5*7+···2005/99*101=?为什么这么做?2005/1×3+2005/3×5+2005/5×7+.+2005/99×1012005/(1×3)+2005/(3×5)+2005/(5×7)+……+2005/(99×101)=2005×[1/(1×3)+1/(3×5)+1/(5×7)+……+1/(99×101)]=2005×(1/2)×(1-1/3+1/3-1/5+1
因为分子相同,分母有规律.提出分子后,分母都可以拆成{（1/n）- [1/(n+2)]},整理后,就只有（1-100/101）了.