2010/1 - 2009/2 + 2008/3 - 2007/4 + ... - 1/2010
+ 1/1006 + 3/1007 + 5/1008 + ...+ 2009/2010
= 2010/1 + 2009/2 + 2008/3 + 2007/4 + ... + 1/2010
- 2*2009/2 - 2*2007/4 - ... - 2*1/2010
+ 1/1006 + 3/1007 + 5/1008 + ...+ 2009/2010
= 2010/1 + 2009/2 + 2008/3 + ... + 1/2010
- 2009/1 - 2007/2 - ... - 1/1005
+ 1/1006 + 3/1007 + 5/1008 + ...+ 2009/2010
= 1 + 2/2 + 3/3 + ... + 1005/1005
+ 1005/1006 + 1004/1007 + ... + 1/2010
+ 1/1006 + 3/1007 + 5/1008 + ...+ 2009/2010
= 1 + 2/2 + 3/3 + ... + 1005/1005
+ 1006/1006 + 1007/1007 + ... + 2010/2010
= 1 + 1 + ... + 1 // 2010 times
= 2010
