初中题l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/2005-1/2004I
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 21:36:52
初中题l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/2005-1/2004I
初中题l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/2005-1/2004I
初中题l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/2005-1/2004I
l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/2005-1/2004I
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2004-1/2005
=1/2-1/2005
=2003/4010
=1/2-1/2005=2003/4010
方法;因为 l1/3-1/2I=1/2所以l1/3-1/2I=1/2-1/3以此类推下去
l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+......+I1/2005-1/2004I
解=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2004-1/2005
=1/2-1/2005
=2003/4010
1/2-1/3+1/3-1/4+1/4-1/5+......+1/2004-1/2005
=1/2-1/2005
=2003/4010
2003/4010
因为1/3-1/2<0所以|1/3-1/2|=1/2-1/3
同理可得
l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+......+I1/2005-1/2004I
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2004-1/2005
=1/2-1/2005
=2003/4010
原式=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.....+(1/2004-1/2005)...........................(去括号)
=1/2-1/3+1/3+1/4-1/4-1/5+......-1/2004+1/2004-1/2005
=1/2-1/2005
=2003/4010
1/2-1/3+1/3-1/4+1/4-1/5+.......+1/2004-1/2005
=1/2-1/2005
=2003/4010