1/1×3+1/3×5+1/5×7+…+1/2005×2007=(1/2)×2/1×3+(1/2)×2/3×5+(1/2)×2/5×7+…+(1/2)×2/2005×2007=(1/2)×(1-1/3)+(1/2)×(1/3-1/5)+(1/2)×(1/5-1/7)+…+(1/2)×(1/2005-1/2007)=(1/2)×(1-1/3+1/3-1/5+1...