2005/1×3+2005/3×5+2005/5×7+.+2005/99×101
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 02:33:13
![2005/1×3+2005/3×5+2005/5×7+.+2005/99×101](/uploads/image/z/67850-26-0.jpg?t=2005%2F1%C3%973%2B2005%2F3%C3%975%2B2005%2F5%C3%977%2B.%2B2005%2F99%C3%97101)
2005/1×3+2005/3×5+2005/5×7+.+2005/99×101
2005/1×3+2005/3×5+2005/5×7+.+2005/99×101
2005/1×3+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
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