｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=?

来源：学生作业帮助网编辑：六六作业网时间：2024/11/15 21:21:54

｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=?｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009

｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=?
｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=?

｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=?
原式=I1-1/2I+I1/2-1/3I+I1/3-1/4I+...I1/2009-1/2010I
=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010
=2009/2010