【分数】1/1x3+1/3x5+1/5x7+…+1/2009x2011要清楚过程的,乘用x代替,用简便方法计算

问题描述:

【分数】1/1x3+1/3x5+1/5x7+…+1/2009x2011要清楚过程的,乘用x代替,用简便方法计算

1/1x3+1/3x5+1/5x7+…+1/2009x2011
=1/2X【(1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/2009-1/2011)
=1/2x(1-1/2011)
=1/2X2010/2011
=1005/2011