1/2+1/6+1/12+1/20+……+1/2008*2009

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1/2+1/6+1/12+1/20+……+1/2008*20091/2+1/6+1/12+1/20+……+1/2008*20091/2+1/6+1/12+1/20+……+1/2008*20091/2+

1/2+1/6+1/12+1/20+……+1/2008*2009
1/2+1/6+1/12+1/20+……+1/2008*2009

1/2+1/6+1/12+1/20+……+1/2008*2009
1/2+1/6+1/12+1/20+……+1/2008*2009
=1-1/2+1/2-1/3+.+1/2008-1/2009
=1-1/2009
=2008/2009

原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5...+1/2007-1/2008+1/2008-1/2009
=1-1/2009=2008/2009
你看对不？

原式=1/2+1/2*3+1/3*4+1/4*5+......+1/2008*2009
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/2008-1/2009
=1-1/2009
=2008/2009

原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5...+1/2007-1/2008+1/2008-1/2009
=1-1/2009=2008/2009