1+2-3-4+5+6-7-8+...+2001+2002-2003-2004
=(1+2-3-4)+(5+67-8)+...+(2001+2002-2003-2004)
=(-4)+(-4)+...+(-4)
=(-4)*501
=-2004
1/1*3 +1/3*5 +1/5*7 +...+1/99*101
=(1/2)(2/1*3 +2/3*5 +2/5*7 +...+2/99*101)
=(1/2)[(1/1-1/3)+(1/3-1/5)+...+(1/99-1/101)]
=(1/2)(1/1-1/101)
=50/101
(1/2005 -1)(1/2004 -1)...(1/3 -1)(1/2 -1)
=(-2004/2005)(-2003/2004)(-2002/2003)...(-2/3)(-1/2)
=(-1)^2004*(2004/2005)(2003/2004)...(2/3)(1/2)
=1/2005