1/2+1/6+1/12.+1/2011*2012

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1/2+1/6+1/12.+1/2011*20121/2+1/6+1/12.+1/2011*20121/2+1/6+1/12.+1/2011*20121/2+1/6+1/12+1/20+...+1/2

1/2+1/6+1/12.+1/2011*2012
1/2+1/6+1/12.+1/2011*2012

1/2+1/6+1/12.+1/2011*2012
1/2+1/6+1/12+1/20+...+1/2011*2012
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2011-1/2012
=1-1/2012
=2011/2012

1/2+1/6+1/12.....+1/2011*2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012

1/2+1/6+1/12.....+1/2011*2012
=1/1*2+1/2*3+1/3*4+...+1/2011*2012
=1/1-1/2+1/2-1/3+...+1/2011-1/2012
=1-1/2012
=2011/2012

1/2+1/6+1/12.....+1/2011*2012
=1-1/2+1/2-1/3+……+1/2011-1/2012
=1-1/2012
=2011/2012

1/2+1/6+1/12+1/20+...+1/2011*2012
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2011-1/2012
=1-1/2012
=2011/2012