1/(11×12)+1/(12×13)+……+1/(2009×2010)=

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1/(11×12)+1/(12×13)+……+1/(2009×2010)=1/(11×12)+1/(12×13)+……+1/(2009×2010)=1/(11×12)+1/(12×13)+……+1/(

1/(11×12)+1/(12×13)+……+1/(2009×2010)=
1/(11×12)+1/(12×13)+……+1/(2009×2010)=

1/(11×12)+1/(12×13)+……+1/(2009×2010)=
原式=1/11-1/12+1/12-1/13+.+1/2009-1/2010
=1/11-1/2010