Question

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

Answer 1

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

Answer 2

1/2-1/3+1/3-1/4+1/4-1/5+......+1/2004-1/2005
=1/2-1/2005
=2003/4010

Answer 3

2003/4010

Answer 4

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

Answer 5

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

Answer 6

1/2-1/3+1/3-1/4+1/4-1/5+.......+1/2004-1/2005
=1/2-1/2005
=2003/4010