初中题l1/3-1/2I+I1/4-1/3I+I1/5-1/4I+.+I1/2005-1/2004I

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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

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