1/1×3+1/3×5+1/5×7+…+1/2009+2011=?
原式=1/（1×3)+1/(3×5)+1/(5×7)+.+1/(2009×2011)
=(1-1/3)×1/2+(1/3-1/5)×1/2+(1/5-1/7)×1/2+...+(1/2009-1/2011)×1/2
=1/2×(1-1/3+1/3-1/5+1/5-1/7+.+1/2009-1/2011)
=1/2×(1-1/2011)
=1/2×2010/2011
=1005/2011
用括号是因为在网上分数线是斜着的,这便于看