Question

1x3分之1十3x5分之1十5x7分之1十.十2009x2011分之1十2011x2013分之1=?

Answer 1

1/(1x3)+1/(3x5)+1/(5x7)+...+1/(2009x2011)+1/(2011x2013)

=(1/2)x(1/1-1/3)+(1/2)x(1/3-1/5)+(1/2)x(1/5-1/7)+...+(1/2)x(1/2009-1/2011)+(1/2)x(1/2011-1/2013)

=(1/2)x(1-1/3+1/3-1/5+1/5-1/7+...+1/2009-1/2011+1/2011-1/2013)

=(1/2)x(1-1/2013)

=(1/2)x(2012/2013)

=1006/2013