[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 15:47:34
[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]

[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]
[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]

[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]
[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]
=(1+2010)*(2010/2)/((1005/1006)(1006/1007)...(2008/2009)(2009/2010))
=2011*(2010/2)/(1005/2010)
=2011*2010
=4042110

[1+2+3+4+5+...+2009+2010]/[(1-1/1006)(1-1/1007)...(1-1/2009)(1-1/2010)]
=[(1+2010)×2010/2]/[1005/1006×1006/1007×...×2008/2009×2009/2010]
=2011×1005÷1005/2010
=4042110