1/2+2/3+3/4+...2005/2006简便计算

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 01:08:22

1/2+2/3+3/4+...2005/2006简便计算
1/2+2/3+3/4+...2005/2006简便计算

1/2+2/3+3/4+...2005/2006简便计算
=1-1/2+1-1/3+……1-1/2006
=2007-(1+1/2+1/3+……1/2006)
=2007-(ln2006-γ)
≈2007-7.603897968521880840282817113051-0.57721566490153286060651209
≈1998,8183879863021289979668922264

=1-1/2+1/2-1/3+1/3-1/4+1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006