1/1X2+1/2X3+1/3X4+……+1/2012X2013

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1/1X2+1/2X3+1/3X4+……+1/2012X20131/1X2+1/2X3+1/3X4+……+1/2012X20131/1X2+1/2X3+1/3X4+……+1/2012X20131/1X

1/1X2+1/2X3+1/3X4+……+1/2012X2013
1/1X2+1/2X3+1/3X4+……+1/2012X2013

1/1X2+1/2X3+1/3X4+……+1/2012X2013
1/1X2+1/2X3+1/3X4+……+1/2012X2013
=1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013
=1-1/2013
=2012/2013