1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2011-1/2012=1+(-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2011)-2012=1+((-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+...+1/2011))-2012=1+(0)-1/2012=2011/2012
=2011/2012
1-1/2012=2011/2012
1-1/2012=1/2011