2乘以4分之一+4乘以6分之一+6乘以8分之一+...........+2012乘以2014分之一等于

解：
原式

=1/2x(1/2-1/4)+1/2x(1/4-1/6)+1/2x(1/6-1/8)+……+1/2x(1/2012-1/2014)
=1/2x(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2012-1/2014)
=1/2x(1/2-1/2014)
=1/2x(1007/2014-1/2014)
=1/2x1006/2014
=503/2014 （2014分之503）

=1/2x(1/2-1/4)+1/2x(1/4-1/6)+1/2x(1/6-1/8)+……+1/2x(1/2012-1/2014)
=1/2x(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2012-1/2014)
=1/2x(1/2-1/2014)
=1/2x(1007/2014-1/2014)
=1/2x1006/2014
=503/2014
观察规律，诸如此类问题很好解答

=1/2+2/3+3/4+……+506/507
=(1-1/2)+(1-1/3)+…+(1-1/507)
=506-(1/2+1/3+…+1/507)
=507-(1+1/2+1/3+…+1/507)
=507-ln507
≈507- 6.23
≈500.77

参考自http://zhidao.baidu.com/link?url=0neeuWoYeqprsLHFEPRFyBy86SbUkpNmbHNY4JoA2fI7wT4Hlmpfaba8EyWXGvEUU9WNYu7jG2FTp-hV2YRBcK